For Animus Summons, their cultivation was extremely unique!
Their Summoners did all the work as they cast powerful Trainer skills that directly caused essence to flood into them and elevate them to a higher level, the job of the Summon only being to consolidate and stabilize their realm before they can move forward.
Common ranked beasts took a long time to refine their new realms before they could advance to the next rank even with the aid of [Animus Growth Empowerment], with rarer Summons taking a shorter amount of time.
The truly rare or Ultra Rare Summons with powerful Archaic Bloodlines would take even less time before they could refine and consolidate their new Realms, being some of the beasts that could be raised extremely fast!