In the context of Many Worlds, a "universe" is an approximately classical wave function, where the degree of approximation is limited by the uncertainty principle.

Even if you start with an approximately classical wave function, it may evolve into a state where it is no longer approximately classical. However, it might now be equal to the sum of _two_ approximately classical wave functions. Ie, two "universes".

So, the universal wave function hasn't split, but the attempt to represent that wave function by approximately classical wave functions _has_ split.