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.

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Your cities that haven't yet converted will feel some passive pressure to spread, but it's not very fast. If you're planning to choose beliefs that help your cities, then consider faith-buying some missionaries to do spreading domestically. I wouldn't delay adopting your 2nd belief; getting it sooner means that you'll have better choices.
 
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