I just did one of the invasions on my pally then tried to do the same one on my warlock but Sergeant Crowler didn’t have the quest after turning in the quest I got from the missive. Do I need to buy a different missive or are they just not guaranteed to happen?
You can do an invasion once per week on each character who has unlocked invasions in their Garrisons. You will receive the introductory quest when your Garrison is upgraded to Tier 2 → Horde quest / Alliance quest.
The amount of mobs that need to be killed in an area in order to trigger them attacking via invasion will vary.
More info can be found in the Wowhead guide:
Just a PSA re this. Ever since the original level squish, a lot of the garrison invasions are kinda borked in that when you start them, they will simply not spawn enough mobs for you to get platinum rank (which gives you 2 chances for a mount). The only assault that spawns enough mobs to get the requisite points is Magnarok. I haven’t tested all of them but from the ones that I have, they won’t spawn enough mobs during the invasion.
So be careful which invasion you activate if you want 2 chances at a mount per character.