Did you speak to the nursery worker after, OP?
I work in early years and wouldn’t personally shout in a child’s face, but unfortunately it is quite common and I do see it a lot.
However, if I had had to speak to a child whilst a parent was still there, I certainly wouldn’t expect that parent to just leave without first speaking to me about the child’s behaviour and also speaking to their child to reaffirm that we don’t behave like that in nursery. You are the parent here, OP. It shouldn’t be left to nursery workers if you are still present.
What I will pick up on is your attitude to him being “wild” and splashing water being “that’s all”. Splashing water may be cute and funny at home, but at nursery it ruins other children’s play and can upset them and that is NOT okay. No child should be disrupting the play of others. There will be different and firmer expectations at nursery than at home because they’ve got so many children with varying needs to deal with. His “wildness” will therefore have more of an effect at nursery than at home. What seems like a “that’s all” situation at home won’t be when it affects a bunch of other children. You need to have a firm chat with him to reaffirm expectations at nursery.
Also, I don’t understand how he was able to go and splash water whilst you were there? No child should be behaving that way whilst their parent is there as you should have still been parenting him at that point.
Also, the fact your son is behaving in a way that he needs to be spoken to immediately upon entering the nursery is a major concern. That would be more of a concern to me than the way he was spoken to. He is going to come across many teachers/childcare workers who speak to him more firmly than you would. Have they tried other menthols first that don’t get through to him, since this behaviour is still occurring?