Jon/Julie remembered the note that came with the stone. "Changes made will be as if it has always been so, apart from for those within earshot of the wish..."
You could change that by saying "I wish that everyone remembers" or "I wish that nobody remembers"--but Joseph didn't say anything like that. If you don't, everyone who hears the wish knows what happened. Joseph heard his own wish. So he knew that his girlfriend was really Jon.
He was just pretending. He must have made the wish, seen Jon turn into a girl, and figured out what happened. Jon realized that Joseph must have made up the name Julie.
But for some reason, Jon wasn't angry at Joseph. (He didn't realize it, but that was the effect of the wish--Joseph wished she would have a personality he could get along with. Someone who would get angry and refuse to be his girlfriend after one minute with him wasn't someone he could get along with.)
In fact, thought Jon, Joseph deserved a break. If Joseph wanted a girlfriend there was no harm in being one for a while. And she had to fix the name. "I wish that until I change back my name really is Julie, and that nobody else including Joseph remembers that I made this wish."
"Hey, is something wrong?" said Joseph. "Sorry about the name, it just slipped out... I..."
"What do you mean? Julie is my name."
"Oh... it is? I mean, of course it is!" Jon--now Julie--kissed Joseph back....
