Thank you all for your kind replies!!!
I spoke to the lady who's the bus monitor (all kids are being picked up at the front of the gate to the housing and transported to the school and back, which is ~ 10 min. away -it's a small bus for ~ 20 people, not a real big one!) and also coordinator between Americans and Italian school. She said not to worry and that accidents happen; so I guess I might have felt the pressure on me completely by my own fault.. Furthermore she explained that the kids are being brought to the bathroom every 30 min., so it's not that they expect the little ones to do it on their own necessarily. I spoke to a few other parents and one said, her DD wasn't comfortable (yet?) going to the bathroom there and she tends to hold it.. Maybe it's the same with DS, only that after a while he can't hold it any longer? I'm not too sure though as I've seen the evidence that he's done #2 over there [I guess nobody helps/checks? to wipe as he's not able yet to do it by himself..]...
After the day I originally posted this thread I didn't talk much with DS about the incident, wanting to just give him some peace and surprisingly, the next day there were no accidents!.. Did I make too much pressure with my previous talks with him? I don't know, but now that I know that the teacher doesn't expect a young child his age to fully be potty trained and rather count on accidents, I'm more relaxed myself too.
It was helpful to me to read your responses; especially from those of you who're in the school business and have more insight from that level! (Thank you, mataji4)
I decided that we won't use pull ups on him as I'm afraid it might set him back (after all, he seems to be more lazy as a boy; when he wears a pull up, he pees in it and doesn't bother going to the bathroom!..) and simply include another extra set of spare clothes!
All in all, after having read your comments and giving the subject some thinking plus the talk to the lady, made me really relax more and just accept it as it is! The least I want is to put pressure on my child!!!
Thank you all again!!!