I've not seen that happen yet.It gets really weird when they take a city, then have their original city captured.
Not once have I seen a CS take a city in any of my games no matter how many units I've given them... It's very annoying!
In my game the CS puppet stayed at pop 1 like the problem city.Hmm this gives me an idea. CSs have a basic prince level difficulty no matter your setting I think, so making that deity.. might mean they'll puppet everything. Add patronism, and you get one heck of a science level.
Not once have I seen a CS take a city in any of my games no matter how many units I've given them... It's very annoying!
It may have something to do with their personalities, some of the more aggressive CS are more likely to go on a killing spree. I've seen CS keep cities as well.