The wish stars you find at Star Hill and can subsequently take on as "side quests" are those that have already passed through Star Road and fallen back to the world. Those wishes have already been granted, it's just not an immediate effect.
For example, the wish
"Please let Mallow find his way home"
had already been granted by the Star Road prior to Exor crashing through it, and was going to happen. Fate was in motion for that one -- Mario's journey was the vehicle for that wish to come true.
The Star Road is necessary to grant wishes, but it's not an immediate, magical effect. It's more like it adjusts the timeline so the wish will happen at some point in the future.