Simply put, such a building permit could specifically exclude some residents from "residents only on-street parking" through language that mandates that all owner parked cars of a given new development must be accommodated on the private property directly associated with the project.
Thus (perhaps) no permitted street parking for newer buildings with such agreements in place, and permitted street parking for other (older, as per Ismo) buildings with no such agreements in place?
A building permit can't change a bylaw, Council needs to adopt an amendment bylaw to do that. Just because the BP includes on-site parking that meets the parking rates in the Zoning Bylaw, doesn't mean that residents of that building can't use the street parking if they choose. Otherwise, anyone with a garage or driveway technically wouldn't be allowed to park on the street either.