My understanding is that cities picking up your religion upon founding is normal. The city that you founded your religion in becomes the Holy City for that religion, and will definitely adopt that religion. I don't recall from previous plays if having a Holy Site in a city will also cause them to adopt upon founding, but I would think that's likely.
You can find more information here:
You can find more information here:
Religion (Civ6) | Civilization+BreezeWiki
breezewiki.com