"Plotting war" and "plot culture" are two different things - one refers to plans, the other refers to tiles.
As far as I know there's only plot culture, which determines which tile belongs to which civ to what extend, and city culture, which determines how many rings of culture a city has and how much it contributes to plot culture.
Partially random chance, even if AIs don't cheat the RNG they can still get lucky, but in this case I suspect that religion is a factor. Revolt chances are usually pretty low, something like a 20% chance to revolt is huge in most cases, but if a city has your state religion present it reduces the revolt chance by a flat 5%. Usually this is enough to completely cancel a revolt chance, or at least severely mitigate it, so that AI city was fine. If an AI city that's wanting to flip to you has your state religion in it, however, the revolt chance increases by 5%, so that might explain why your city was gone instantly if you got a religion spread and didn't adopt it as your state religion. If both are present both modifiers just cancel each other out, FYI.