Not really, the ascians spread an established knowledge, the primals are not their creation, some summoning have happened by accident in the past, when a certain tribe felt threatened as such ending the ascians will not remove the primal problem completely.
Ending the Garlean campaign will help, but if you consider the summoning of Susanoo it's not a certain thing.
With the right condition any small territorial squabble might lead to a summoning.