(SPOILER)Keep in mind that the secret world was happening at the same time as the actual world. There were also two Joshua's. Joshua had a hard time accepting anything different, and he had not yet returned to see the Real Neku who proved to him it was worth leaving as it was.

As for whether or not he played another week, the answer I see is no, he did not. Joshua was testing him, and he passed. The reason it says a week passed is because they promised to meet on a Sunday, and I'm guessing that they probably were returned at the beginning of a week. So they had to wait til the next week to actually meet.

All in All, love the game

THE JACKEL