I am actually really curious about this as my daughter (level 7 rising 8) has been trying to get her back twisting for a while now. She doesn't twist until the very end and therefore crashes (onto a resi) and fears it. We are trying out new gyms this week and once established she really wants to work on fixing this mental block. Are there actual progressions for twisting? All she was ever told was just do it.
Sorry, I meant to respond to this back when you posted it and then got sidetracked, and randomly remembered just now. And since I rarely pass up an opportunity to nerd out about technique and mechanics, this will probably end up being a gigantic wall-of-text.
I'm gonna give a two-part answer here, one for the progression, and two for the technique and the "just do it" approach (tl;dr: "just do it" in teaching twisting is not the approach I'd use, but it's a more viable approach than it may seem).
PROGRESSIONS:
Here are my favorite progressions for twisting, which should be done entirely on a trampoline with a mat thrown in for the landing. Steps labelled #a and #b are trained in parallel.
1a) 3/4 back layout to stomach
1b) 3/4 front layout to flat back, watching the mat all the way until the landing
Note: in both of the above skills, the arms should be up on takeoff, then move out to a T-shape and then down towards the athlete's sides as she rotates the salto.
2a) 3/4 back layout with LATE half twist (spot the ground before twisting), landing on back on trampoline
2b) 3/4 front pike-open to flatback, watching the mat until landing
3a) Back layout with LATE half twist to feet. Spot the mat before twisting
3b) Front pike-open with LATE half twist
4) 3/4 back layout with slightly earlier half twist, focusing on visual cues. Athlete should first see the wall in front of them, then see her toes, then do a quarter turn and briefly spot the landing, then finish the salto/twist to land on the back. The idea is that the twist should happen roughly between 1/4 and 2/3 of the way through the salto. Too late is better than too early.
5a) Back layout with sort-of-but-not-really-early half twist to feet (timing and visual cues are the same as in 4)
5b) Front layout with LATE half twist
6) Back layout 1/1
Notes:
In any front 1/2 or back 1/1, the athlete should be able to see the ground for pretty much the entire skill. When first learning, they may lose sight of the ground very briefly about halfway through the salto, just before initiating the last 1/2 twist (since twisting too late is preferable to twisting too early), but as they get accustomed to the skill they should be able to see the landing the entire time. When done properly, it's the least-scary skill in the world, and the easiest to land cleanly, because seeing the ground means you always know exactly how high you are and exactly how fast you're rotating, and this will become extremely important in twisting multi-salto skills.
There is another important and I think often-underemphasized point of focus on front 1/2 and back 1/1: these skills should both feel extremely slow, leisurely, and lazy. The athlete should not feel like she is cranking the twist around; she should feel like (after initiating the salto and twist) she is just lazily drifting through the air while watching the ground, waiting for the landing. When the skill feels leisurely, it becomes very easy for the athlete to focus on body position and make any necessary corrections to form and body alignment.
7a) Front tuck 1/2 (done from a low bounce, without the pronounced kick out than earlier front twisting progressions. This is not done with the intent of actually using a front tuck 1/2 as a skill, but as prep for twisting multi-salto skills, such as yurchenko 1/1 or double back 1/1-out)
7b) Front layout 1/1. Spot the ground before the final 1/2 twist (more details down below)
8) Back layout 3/2. Spot the ground before the final 1/2
9a) Front 3/2.
9b) Back 2/1. Athletes very commonly start twisting early at this stage and lose control of the salto, so it is SUPER IMPORTANT that the athlete sees the wall in front of her as she takes off before initiating the twist.
10) For front 2/1 and 5/2, as well as back 5/2 and 3/1, there's nothing new to the technique; it just has to be higher and more aggressive.
11) For front 3/1, back 7/2, and beyond, there are some top-level optimizations necessary, and the athletes generally have to start using a torque-on-takeoff technique. I won't bother digging into the details here because it's irrelevant to 99.9% of athletes. But if you ever wanna see some really funky-looking roundoffs and backhandsprings, watch Kenzo Shirai's back 4/1. His crooked tumbling for big twisting skills is not a mistake, it's a deliberate top-level optimization.
TECHNIQUE/MECHANICS:
This is sort of complicated, and there is a long list of exceptions and caveats to anything I could possibly say about ideal twisting technique. Twisting technique can be complex and vary a lot depending on the context, and there are three different ways in which it is mechanically possible to generate twist. I'm only going to get into one of those three methods here, because I think the other two are usually suboptimal, and because this post is enough of a wall-of-text already.
To a certain extent, athletes have to learn to intuitively feel how to twist without actually thinking about the specifics, which are too fast and too variable for them to have enough time to consciously focus on each element and position. Because of this, many coaches find it easier to just tell the athlete to twist, and leave it to the athlete to figure out how to actually make the twist happen intuitively, rather than trying to teach the athlete to be deliberately aware of the specifics of the technique. So "just do it" is not as crazy as it sounds.
Having said that, I prefer to teach the athlete to deliberately focus on what I would consider optimum technique; however, I do this knowing that as the athlete progresses, that deliberate focus will fade and the athlete will subconsciously make individualized changes to their twisting technique that work for them. This deliberate approach to twisting technique is undoubtedly a slower process for most athletes, but I think it leads to more precise and consistent technique in the long run.
Here's how I prefer to teach the specific technique, with the disclaimer that this is one of a thousand or so workable ways of teaching twisting. I'll describe this for an athlete who twists left, so reverse all of this if you're talking about a right-twister.
1) For back 1/2, the athlete has both arms up during the initial phase of the salto, then brings the left arm (the one they'll be twisting toward) out to the side, then down to join the rest of the body. This asymmetry causes the body to tilt slightly off-axis in the salto, which converts a small amount of flipping momentum into twisting momentum. Just before landing, both arms should move to a roughly 30 degree angle up and out, forming something between a "Y" and a "T" shape. Arms remain straight the entire time. For the back 1/2, the landing should ideally have the palms turned upward, the chest open, and the chin slightly up.
2) For front 1/2, after takeoff the athlete should move both arms (completely straight) out to that same low-Y position described above. From here, the right arm continues all the way down to the side of the body, while the left arm remains up and out. Just before landing, both arms are brought out to low-Y position, though unlike the back 1/2 the chest should be slightly hollow and the arms can be lower and more in front (closer to what you might expect when sticking a landing).
Note: For both steps 1 and 2, the arm movements are deliberately exaggerated way beyond what is necessary or optimal; the idea is to train the athlete's intuition. We want the athlete to reach a point where they think "twist," and their arms intuitively make the correct movements to initiate the twist, without them having to actually think about the specifics. In time, these movements will naturally become less exaggerated and more efficient.
3) Once the athlete has a feel for how to initiate the twist going forward, she should then learn front layout 1/2 with both arms coming all the way down to the side during the rotation. One arm will still come down before the other to initiate the twist, but at the point the difference should be a bit more subtle than in previous steps.
4) For back 1/1, the athlete should combine the first half of step 1 (back 1/2) with the second half of step 3 (front 1/2), resulting in a clean, leisurely back 1/1 with arms by sides where the athlete can see the ground for the entire time after the first 1/4 twist. I know I have already said this, but it's worth repeating: visual cues are extremely important. The athlete should see the wall in front of them as they take off, then see the toes before initiating the twist, then see the landing after the first 1/4 twist, then watch the landing for the remainder of the skill. If the athlete finds it scary, it is almost certain that she is not using correct visual cues; if she sees what she should see, the skill should feel easy and leisurely and lazy.
5) For front 1/1 and back 3/2 the takeoff and twist initiation are the same as I described above. Once the salto and twist are initiated, the athlete can either rotate with the arms straight by the sides or with the hands pulled toward the chest -- either way works fine.
After the first 3/4 of a salto, the athlete should have completed the 1/2 (if forward) or 1/1 (if backward), and have her eyes on the landing. For the final 1/4-salto and 1/2-twist, the athlete should lead the twist with the toes, with the head watching the ground as long as possible and being the last thing to turn. The right hand should reach towards the floor beneath them, while the left elbow should pull towards the ceiling; at this point, the athlete should have done all but the last 1/4 twist.
At the last moment, right as the athlete completes the final 1/4 twist, she should move her arms to the now-familiar low-Y shape, with the palms turned upward, the chest slightly open, and the chin slightly up.
6) For twisting beyond this, not much changes about the takeoff or the last 1/2-twist; it's just about fitting more twists in between them. The one change is that from here on up, once the twist is initiated the athlete should pull the hands to the chest, instead of twisting with arms straight by the sides. Two reasons for this: first, it's easier to keep the arms in this way, which becomes increasingly important as centrifugal force increases with twist speed (side note for my fellow physics nerds: yes, I know centrifugal force doesn't actually exist as a force, I'm using it colloquially to refer to the feeling of being pulled outward during rotation). Second, it makes it easier to bring the arms up on landing for a stick or a connection.
For skills landing backwards (such as a back 1/1 or front 3/2), the athlete should try to maximize the height of the skill, and try to see the ground at the end as they prepare for a controlled landing.
For skills landing forward (at least on floor), athletes should not strive for a controlled stick. Athletes should prioritize distance over height, in order to maintain momentum into a subsequent skill.
As an abstract ideal, I would tend to shy away from finishing a tumbling pass with a single salto skill that lands forward, because such skills are better-suited for connecting into another skill (for example, back 3/2 front layout). But this is an ideal, not a rule; in the real world, you tailor the routine to fit the athlete's current abilities, and sometimes that means landing forward.
(I think down the road I might edit this and use it for a Technique with Taucer article)