Revolting cities clarification

[temporyacc]

So I know if a world ideology is passed and if a civ isn't following that ideology and their approval rating is high enough their cities will start defecting to a civ with a high enough influence. But I'm not sure what the actual mechanic is. In my current game I'm Portugal (freedom) and my neighbor is Rome (order) I passed the world ideology of freedom so he's in civil rebellion and my culture is at the influential level over his. Why won't his cities defect to mine?