When Josh went back to being a kid again, an adult named Josh Baskin dropped off the face of the earth. This wouldn't be a problem if he was a nobody, but in his short time as an adult, he did quite a lot to get remembered. He leased an apartment, got a job, and then by virtue of his kiddish nature and his skills on the giant piano, he climbed the corporate ladder to an executive-level job in a matter of weeks. He made friends, acquaintances and business contacts along every step of the way.
As far as those people are concerned, he just disappeared, with no warning. Didn't somebody go looking for him? There must have been a police investigation, during which time the cops surely noticed there was already a missing Josh Baskin in the area (a kid) who was reported as found right when the adult Josh Baskin disappeared.
Now, we're not saying they would be able to just put two and two together and decide it was all a magical conspiracy, but it would certainly raise questions. Between looking for the adult Josh and following up with the kid Josh, they'd have to talk to his friends, family, coworkers, etc.
Frankly, his tailor earned some jail time.