I wouldn't choose to have my dog in that class at this particular time with the situation as described. I don't think you are worrying unneccesarily. Trust your instincts.
What you have described worries me.
I dont think that a training class should be large, esp with puppies. If the dogs are all that reactive, then the trainer is not doing their job. (If its a large class with a bunch of dogs, there is no way for them to do their job properly)
This sounds almost like one of those Petsmart or Petco "training classes". I've helped "correct" the poor skills resulting from those classes, including pups that ended up fearful from all the chaos, or thinking that training time was romper room. Puppies end up confused and owners frustrated, and THAT is a terrible combination!
I would have to pull out, and hope for a refund or a transfer to a smaller class more suitable to your needs.