What's this parade feature mentioned in the serebii page?
After your avenue (the avenue itself, not the shops in it) reached Rank 20, you'll be called into the office, and the owner will make you do a parade in the avenue.
The parade can be reactivated later on at any time by talking to an NPC inside the office.
It's nothing interesting, really.
You just automatically walk along the path of the avenue. And while you walk, each shop's description along with when they start opening the shop is mentioned, complete with fancy sound effects.
Then after all shops are mentioned, each of your secretaries are shown in the same way. That's all.