That doesn't really explain the mechanics of the splitting process.
It's "And to explain this, we postulate that a whole new universe appears fully formed out of nowhere, with an identical history but a distinguishable future, because it does."
I suppose it's possible. But it doesn't seem very parsimonious - because you effectively have to double the energy in the multiverse for every distinguishable quantum event.
Does conservation of energy not apply in the multiverse? Are universes - as many as you need - free at point of sale?