I think the shop owner just thought Naruto was running errands for his elders like a good boy. After all, Naruto was going to all of those different shops and getting a lot of stuff. Plus getting an adult sized treat along with the normal one automatically gives the impression that the kid is getting the big one for an adult.
BTW, does anybody else think that the current appearance of Tsunade looks exactly like her young one (in flashbacks)?
It shouldn't be too hard for Jiraiya to recognize her.