This is a bit of a classic pattern with children who start late in the school year. Often, friendship groups are already established, and some of the older children who are going to school in September are well and truly ready to move on, IYKWIM.
The first important thing here is that your DS is 'dealing with it well', so we assume not getting distressed or angry / aggressive about it. Good for him. But if I was you, and the nursery assistant says 'he dealt with it very well', I would say 'Can you explain what you mean? What did he do?'
Secondly, whilst I'm a great believer in letting them sort out minor disagreements themselves (and often even young children can surprise you at how well they can do this), they are still only 3 and 4. If it's a 'few times' that this has happened, I would suggest that you ask them about their approach. You can be very calm about this, just say 'As staff, how do you usually handle a situation like this?' and see what they tell you.
IME (both as a parent and working in EY), the children who start in the summer term often come up against this sort of thing, but it tends to all sort itself out in September. Come the autumn, there's a whole load more new starters, and children like your DS suddenly become old hands at the whole thing.