response in generalInvoluntary body shaking in sitting meditation can be perfectly normal. The Buddha talks about it in this sutta SN 54.7:
Shaking and vibration can range from mild, like nose or mouth twitching, to strong and even violent shaking, but with persistent correct meditation done over a long period of time, the energy will smooth out and eventually shaking will disappear. Doing yoga, accupressure, other healing health modalities can accelerate the smoothing of the energy flow.
Naturally, the more violent the shaking, the more scary it looks to outside observers, and the more worried they are. Probably most assistant teachers don't have personal experience with shaking and vibration, and are not taught how to deal with the situation.
But with that said, meditation can trigger serious mental health issues, with or without body shaking, and even for people who've been meditating a long time and getting the expected positive results. So it's reasonable for assistant teachers, and even expert meditation teachers with tons of experience, to take precautions to err on the side of safety. If in any doubt, check with qualified professionals. Safety first.