I don't know if it's 'normal' but it's probably fairly common.

I'd go and chat to them. They'll probably be a bit embarrassed to be confronted with you face to face and with such a reasonable attitude about it - 'just let us know and we'll deal with it etc'.

I think its about the attributions people make about situations and other peoples behaviours. They were probably a bit annoyed that your trees were overhanging their yard (for whatever reason). They may have made a few wrong assumptions that a) you knew the trees were growing over their fence; b) you didn't care about it (because they noticed it and then you did nothing for however long) and c) that you were not going to do anything about it. I think when people feel personally injured by others (or by a situation) they tend to make false attributions about the other party that the behaviour was intentional and specifically designed to upset them. It seems rare to find people who's first thought is to take the most positive and innocent view of things.

I wouldn't go into all the reasons you are annoyed about their behaviour because they'll only feel attacked (unjustly in their mind) and retaliate. I'm sure in future they'll let you know if you tell them you do see it as your responsibility (You're very good to do that btw, I think it's far more common that people feel whatever is in a properties airspace is their responsibility and likely the neighbours will have past negative experiences).

My parents have a neighbour who walks dogs and everytime they are out, they come home to dog doo in their backyard. They can't prove it was her but she only lives three doors away, is walking dogs multiple times every day and it's only when they are out. Now I find that weird that she would let them into someone elses backyard and then not clean up after them......