It's not standardized from gym to gym.
I'm no longer coaching, but when I was, I wasn't a particular fan of "fast tracking" kids in most circumstances. If you're taking a young and talented kid and trying to get them to a high level as fast as you can, that to me feels like a high-risk/low-reward endeavor. Just because they can doesn't mean they should.
That said, I do believe in making sure talented kids are still challenged, and usually that takes the form of (cautious) uptraining. If the skills for their current level are clean and consistent, then I'll let them spend time on skills for the next level, pretty much any time except in the week or two before states.
I have only once had a kid skip a level at compulsories, and that was because by the end of level 3/4 summer, she had all her L5 skills better than any of my L5s, was safe and consistent to my satisfaction, and my biggest concern was that she'd get bored and lazy if I had her compete a full season at L4. So she did one meet at L4 and then moved up to L5 for the rest of the season. (Side note: if you keep track of college gymnastics, look out for Lily Goodrich in three years)