A random mob of another species needs to be killed, in addition to a number of mobs of a set species.
Mobs other than those usually associated with NMs are required in addition to the usual mobs
Source:
1. Six hours into an instance, one small group was doing crabs, another was doing worms. There were about 15 people total in the instance. I killed about two to three Zombie Wyverns and the worm spawned and after it was the crab king. Neither had spawned in the six hours prior.
2. After I was the only one left in the instance, I spawned King Igloo after killing a single Mirror Knight. King Igloo was off cooldown for a while. I let King Igloo expire. I was going to attempt to spawn Anapos with random mobs, but decided to wait a minute after Igloo in case it was blocking another NM. In that minute, the billygoat NM spawned.
3. New instance with few players. I killed 26 water sprites and switched to Matamata. Anapos spawned within three kills.
All spawns were as the mob died. The theory makes much sense where Cassie spawns are concernced: Cassie wouldn't spawn because the other mob wasn't being killed. How many groups kill Chimera or Griffins?
The community can compare data to determine further specifics.
Edit:
Here is a vid of #2: https://gfycat.com/BrownCandidAtlanticspadefish
There is a 90 second gap between mob kills
Here is a vid of similar situation to #3: https://gfycat.com/SlightOpenAzurevase
In this one, there are only four other players in the instance and they weren't killing anything.
Going to refine it to: Mobs other than those usually associated with NMs are required in addition to the usual mobs
Wild speculation/ no proof for the following: The lvl and possibly the element of these additional mobs play a part in how much a kill will contribute to progressing a spawn. I doubt it's just a number of mobs or you could have 35s clearing the lvl 20 mobs and spawn NMs faster.
It looks like the first NM to spawn in an instance is easier than the ones that follow, and there are frequent back-to-back NM spawns, where the second one spawns within a minute of the first dying.
I'm thinking there is some kind of priority system and possibly a reset of progress after NMs spawn.
I wouldn't bother with Cassie until more specifics are determined, but you should be able to increase chances of a spawn by (speculation):
1. Entering a fresh instance
2. Having a party or two focus on other high lvl mobs in the area while the main group does Morbols, or assist with Morbols to start and branch off
3. Having everyone else in the instance ignore NM mobs so they don't accidentally spawn one
Ash Dragon: https://gfycat.com/UntimelyMealyBaboon
1/144, didn't start killing demons until a few minutes after the 2hr cd was up. Spawned within 10 kills. Compare how it spawns to the other two clips linked