Well, I think they've got a few choices as how to handle it... Which they could easily implement all of, as an actual choice you make upon liberating/conquering a city.
Some suggestions to that end:
Enslave - The city maintains the characteristics of its founding race, but an 'Upper-Caste' of people from your own society is implemented to keep order and force the peasantry to bend to your will. This could also come with a chance for revolution that could be affected by local military, food, and how much the original inhabitants hate you. (Any one or a mix of those, and I'm sure there are other things you could think of that may or may not factor in to it.)
Purge/Cleanse - Which of these it would be would depend on whether you're 'Good' or 'Evil,' however, and if, that's defined. The city maintains only the look of it's original inhabitants, and only for so long, until finally it's been... 'Adapted,' to your races needs. However, this requires you to move/acquire new citizens for the city.
Liberate - Opposite of Enslave, though not exclusive to enslaved cities. If a city is unhappy enough with its current leader, or was previously enslaved by said leader, and you come in and seemingly save the day for them, you receive a temporary bonus to... Something, build speed, resource production, citizen growth, or any combination there-in. (I say 'seemingly,' because when people want change, and it comes, they generally welcome it with open arms, for better OR worse.) Once the bonus wears off, so does the charm surrounding your liberation, and the city, depending on circumstance returns to a more 'Normal' state of operation.
Integrate - Attempt to integrate that cities population into your empire as a whole, and have a chance to provide a bonus or penalty for an (un)successful integration. There would also be an chance for there to be no bonus or penalty at all, and the chance for the citizens to be more or less neutral to the idea of integration could rise proportionally with how often the city changes hands.
Exile - Exile the current citizenry, allowing them to return to their original empire and giving you control of the city. You would need to bring in new citizens, but you could receive a temporary Prestige bonus in that city, since you showed mercy to your enemy, therefore giving people something to say about you.
There are a million-and-one ways to implement this kind of mechanic, and a million-and-one choices for the mechanic to work on. This is just a very limited sample using what I could come up with off the top of my head.