A Beastmaster's evolution is defined by the advancement of their summoned beast. When the beast reaches certain stages in its evolution, it allows its Master, through the Connection Crystal, to reach new heights.
It is a joint effort between the two.
But it is all thanks to the Connection Crystal and the beast's evolution.
People with beasts that start at advanced evolution stages have a better chance of reaching higher evolutions, especially if their evolution talents are Level 3, 4, or higher.
An example of this is Aurora.
When her Poison Spider awoke, it was in its third evolution. Slowly, its body adapted to that advanced evolution, and when it reached its peak, she managed to evolve it again.
In the fourth evolution, it was enough to fill 10 Connection Crystals, and that took Aurora to a new level.
