yes, the AI cheats, it can even leave cities it conquered a few turns ago with a minimal garrison.

now, there's a "solution" to this, put them to the sword. Leave the city, let it revolt, retake it and suppress the populace. You should prepare an army to do this task beforehand (a stack of green troops you want to gain experience before a campaign for instance)

"Apart from public order, sanitation, water system and peace, what have the romans ever done for us ?"
(or something among those lines, quoted from Life of Brian)

"There's two kind of people, those who kill (good honest romans) and those who dig (basically, everyone else)"
Cornelius "Cluster" Brutus, in some Brutii long game...