The pup's just a baby himself and it will take a little while for him to figure things out. As you note, he sees your son up again and straight away thinks play time is on again. That's logical, and fair enough.
Things you could do would include having your son stop and stand still (no temptation or encouragement for the pup then) and tell the pup to sit. Or alternatively, just tell him "leave it" once again. Immediately after, reward him for complying with whichever command was given and then redirect him to something else (that's fun) instead. He should stat to catch on but it's going to take a while for him to figure out.
Other things can include always ensuring that it's your son who initiates play (even with a specific command) and never the puppy. Once again, it will take him a while to catch on to that concept - but once he finally does, you should have a lot less trouble.