I'm not sure if the Mamool Ja, Goblin and Qiqirn actually have a Primal associated with them or not. These tribes are mostly vagabonds without any central structure about them, apart from having small encampments spread about the area. Qiqirns and Goblins are both passive and aggressive towards the adventurers, while the Mamool Ja are hired mercenaries.
That's not to say these beastmen tribes don't have Primals, but so far the game lore has not given any information about them if they do exist. Being that there seems to be no religiously zealous groups among those beastmen, it could stand to reason that the Ascians may try to influence them to summon one, but the beastmen have to be educated and convinced there is actually one.
I don't think the latter scenario will come into play though based on the events throughout the Primal Ex storyline when the Ascians note that the increased powers of the Primals aren't strong enough to stop the adventurers and they need to come up with another course of action.