Playing as the Iroquois, in a war with the Incas, took a few cities- kept the ones in decent positions, razed the ones i wanted to re-site (their layout was awful- cows, wheat & rivers that were in no cities radius) so I ended up with 2 formely Inca cities, and about 5 new ones I built with my own settlers. The 2 Inca cities ended up quite deep within my borders- it was a thin strip of land, and I rushed a couple of temples to avoid a flip and expand borders. Anyways, I signed peace after acheiving my objective- securing a source of coal, which the Incas could not yet see. About 2 turns later, one of my former Inca cities flipped back to them, with its former cultural boundary intact! So now I've got a bloody big pink spot about a quarter of the way into my eastern border! I always thought that once a captured city had expanded its boundaries under your rule, it was safe from flipping.. Anyway. it'll be easy to take back- they dont have saltpetre or horses and I have cavalry.. but still, bit annoying!