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.
Linked issues
relates to 4
MC-252435
Pointed dripstones can generate floating when generating next to ancient cities
Open
MC-165550
Ligthing of slimes and magma cubes becomes dark when they land to the ground
Resolved
MCPE-153524
Mobs can spawn in deep dark biome and ancient cities
Resolved
MCPE-165550
Mobs spawn in my deep dark
Resolved
I don't think that mobs can spawn within ancient cities, even when they extend to other biomes.