I reported a bug report with regard to cultists. Before I could surround the city, and in two or at most three turns, generally flip the city to free. So long as the negative loyalty generated by the cultists brought the total to below zero, I think it used to flip immediately. But even if it didn't flip until the end of the turn, so long as their annual increase in the city loyalty was less than the negative caused by the cultists recruiting, it would still flip. Now, it doesn't appear that the cultists can bring the city to below zero. I've only been able to use cultists to speed up the flipping of a city to a free city when it was already losing loyalty.