Been there too.
My view after a few of these incidents is that it's OK to be told, and I have to accept another parent's need to do this.
For all I know, that small, part accidental slap/kick/shove that my ds was punished for by the teacher might still be deeply upsetting the other child. Whereas my ds will tell me about it, we'll have a talk and if necessary a further punishment he would then put the incident itself behind him.
However, the other child might have been in floods of tears all evening at home. Perhaps she didn't want to go to school the next day and the mother spent all her energy trying to make her feel OK. You never can tell.
So for that reason, I respect the right of the other parent to tell me and would say sorry my ds upset your child, I know about it and I understand the teacher dealt with it but I will have another word with my son.
I wouldn't tell him off again in front of the parent. It would make me feel I was losing control of the situation. I think it's up me to issue further discipline to my son, if necessary, and to do this when I think it's the best time - and that wouldn't be in the middle of the school playground in front of everyone.
I would think it is necessary if the other child is deeply upset. So I would ask the parent if this is the case. If the answer is no, and my son had already been punished once, I would leave it.
HTH