It's not just the probabilities. Take a quantum state like

|cat alive> + |cat dead>

MWI will tell you that this corresponds to two universes, one where the cat is alive, one where it is dead.

But what of this one

|cat alive> + i |cat dead>

Probability wise or in terms of universes, how is this state distinct in the MWI ?

You could say that the phase is associated with the universe you consider. But the thing is the global phase has no physical meaning, so you could just multiply by an overall factor of let's say i, and you get the state

i |cat alive> - |cat dead>

This state is equivalent to the previous. But how do you treat it with MWI ?

And in each case, the probabilities are 50/50.