I've just started these with my girls. They are doing roundoff back flip tuck back.
The first thing I do is make sure they understand how to rotate.
Lie them on the floor flat on their backs with their arms by their ears, then shout TUCK. The gymnasts should tuck in such a way that their bottom is lifted off the floor and the knees come over their head. As their knees come over their head, they should grab their knees (they shouldn't have to move their arms down to their knees)
Next I do the same drill, but from standing. We go to the trampette and pile mats up behind it. They do 3 bounces then a stretch jump up high and backwards. When the coach shouts TUCK, they land on their shoulders on the mats with their knees over their head.
Next I take away the mats and we have a go at a standing tuck back off the trampette. I don't really expect them to get this on their own, it is really just an orientation exercise.
I want them to understand that the somersault is going up and backwards, not just backwards. A big mistake during this phase is throwing the head backwards rather than using the arms aggressively.
Next I'd put a platform infront of the trampette for the gymnast to jump to handstand on, then 'courbette' off the platform to land on the trampette and perform the tuck back.
I won't move on from this until they can do it on their own. (If we had the DMT out I'd use that instead of this set up and have the gymnast roundoff tuck back or backflip tuck back)
We then move to floor. The gymnasts spend a long time just doing roundoff backflip stretch jumps into my arms. If they get it right I turn them over slowly, if they don't, I refuse to turn them over. They must get this bit right in my opinion as it is the set up for the somersault. If they get it wrong it will take a very long time to get the somersault right.
So far I am at the final stage with all but one of my gymnasts - the other now has the tuck back on her own and after following these steps it took her 2 sessions to get it on her own. The others are having more trouble with it though - one throws her head back, one doesn't keep her arms by her ears, another has trouble getting any rebound out of her backflip so she has a long way to go.
I'm sure there are more progressions, but those are the ones I use!
Good luck!