Under "Saladin" in the civopedia, Righteousness of the Faith description is at first vague on that, but if you keep reading, under "Detailed Approach" it says civ will add a holy site to most cities to then add religious building to boost overall city output of culture/science/faith, which does sound like each city has to have the worship building in order to benefit (which makes sense obviously for a minor building). Under Reports>Yields, does it show the same total for that city (10)?