In Everettian Mechanics, decoherence occurs long before the box is opened. The photons in the box interact with the cat. That entanglement with the environment which causes the branching of the wave function occurs then.
The observer that opens the box is already either in a branch where the cat is asleep (to borrow from Sean Carroll) or awake.
The interesting thing to come to understand is that probability doesn't actually seem to exist as a real feature in the universe. Rather, probability is a measure of what observers believe they will or are seeing. Probability, in Everettian Mechanics, is about perception of the universe, not a feature of the universe itself.
There are observers in all probabilities of the experiment, but each observer only observes their world because decoherence interferes with the superposition of the other worlds. Worlds being the entanglement of the entire experimental setup spreading to everything else.
The observer that opens the box is already either in a branch where the cat is asleep (to borrow from Sean Carroll) or awake.
The interesting thing to come to understand is that probability doesn't actually seem to exist as a real feature in the universe. Rather, probability is a measure of what observers believe they will or are seeing. Probability, in Everettian Mechanics, is about perception of the universe, not a feature of the universe itself.