Most of the time, when I've found an ancient city, I've seen dripstone, mobs, water, and lava intruding inside the area. It seems that they have no requirements for spawning besides being in the deep dark, but don't consider if they intrude into other biomes. My suggestion is to either make the deep dark biome be extended by an ancient city, or to give a similar requirement that ocean monuments have, as in they need a certain amount of deep dark to generate.
Attached below is a screenshot containing the seed, coordinates, and F3 menu of the area that I found this in.
This also happened in Deep Dark Experimental Snapshot 1.
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We plan to work on improving this but it is expected that some part of the city can leak in to neighboring biomes
I don't think that mobs can spawn within ancient cities, even when they extend to other biomes.