Through testing I concluded that the drowned mobspawner is only capable of spawning mobs in oceans underwater. But it doesn't work for ocean biomes from 1.12.2.
I made a nice custom underwater temple in 1.12.2 Realms with the intention to be guarded by drowned when the update arrives. So I downloaded my 1.12.2 map from Realms and tested it singleplayer in snapshot 18w11a. Drowned do spawn naturally in the ocean of my temple, spawn eggs also work properly, but drowned mob spawners do not. It even made my game crash a few times while testing.
So there is something wrong with the 1.12.2 to 1.13 ocean conversion.

I also want to suggest something which I am not sure whether its a bug or not, but it would make the new mob a lot more interesting.
Can you please remove the check for biomes and water for the mob spawners? Currently it's impossible to let them spawn in rivers on land or handmade oceans through spawners. Even though they are able to survive on land and swim in rivers. They don't spawn naturally in these locations, so mob spawners would be the perfect solution.