Whenever my son gets into trouble at daycare, I make sure that I talk to him about what happened and why. I always talk about it with the provider in front of my son so that he knows that we communicate. We talk about how he felt at the time, why he responded the way he did and how he could've handled things differently. We explain what we didn't like about his reaction, how it makes the other person feel (words-sad hearts, hitting - soreness) and what he could do the next time. If is was instigated by someone else, we give suggestions as to what to say or to go get the help of an adult. Your son probably just doesn't know what to say so he gets physical.
We do punish for behavior at daycare, to some extent, since we discuss alternatives, etc. The first incident is usually a "freebie," but then we say "now you know how we feel and how to handle it so if it happens again, then you will get in trouble." Nothing severe because they are learning, but a removal of a privilege or time out, etc.
I don't think this is over your son's head. 3 1/2 year olds are a lot more sophisticated than they get credit for. :) Obviously your son knows what your expectations are because he doesn't do this with you. Maybe the daycare doesn't have clear enough boundaries for him or maybe she isn't consistent. If you work together, his behavior may change. If you don't think he is getting the attention or supervision he needs, then I would look elsewhere.
C.