Do they have after school sports at your school? If so, perhaps you could get the kids to sit and watch netball practice etc for 15 minutes, and you'll know that there are adults around.

As a former teacher, I wouldn't personally ask the teacher to keep them in the class for 15 minutes. I always stayed at school at least an hour after kids finished, but not necessarily in the classroom. The teacher might need to get to the school lib before it closes, go to the office to ring a parent, go to a staff meeting.. lots of reasons to have to leave the classroom after the bell, and would then have duty of care issues if the kids are still in the classroom. 15 minutes might not seem like a lot but time can be tight at the end of the school day to get everything done if you are tied to one room.

Good luck, hope it works out. The kids fitness classes sound like a great idea!