Ingymmom: That is a very good question. I actually stepped into this position last year when I began coaching compulsaries at my new gym. What I did was start them off with basics, see how the performed those skills, and kept working my way up. At my gym, if a rec coach is doing something that is too advanced for the gymnasts (and the coach doesn't stop or realize that it's too difficult), my boss will say something to them. Personally, if I try a newer/higher level skill with gymnasts that I am new to working with, I will begin with the basic progression and work the way up.
I agree with what you said about the front tuck situation, and I feel that the coach was in the wrong (In my personal opinion). I would think that if a coach were to walk into a new program, the other coaches would fill them in with what the gymnasts have been working on, and that there would be some sort of training done to introduce them to the program.
If I were a senior staff member in the front tuck situation, I would intervene and say something to the junior staff member (if that was the case). If that was not the case, I think a parent could say something at the end of class, as a sort of constructive criticism--politely stating that the gymnasts have never done these things before. If the situation conintues, after a parent (or multiple parents) has spoken with the instructor, you can always leave a comment/concern with the employee/head coach.
Hopefully that answered your question.