Many-worlds ideologues like Deutsch never had an exact mathematical model of how the different universes interact, or even of what parts of the wavefunction are the universes. By the way, I regret the inflammatory term "ideologue", but neutered terms like "believer" or "advocate" are not strong enough for me. People like Deutsch combine aggressive advocacy for the correctness of the many-worlds interpretation (MWI), while not having a rigorous concept of what a "world" is.
A layperson hearing about quantum mechanics, through all the homely examples like the cat that is dead and alive at the same time, will naturally think that wavefunctions or quantum states naturally consist of a weighted sum of world #1 plus world #2 plus world #3... but it's not that simple. Partly it comes back to the uncertainty principle, e.g. the trade-off between knowledge of position and knowledge of momentum (which is mass times velocity).
To go from a general wavefunction, to position probabilities, you can break the wavefunction down into a sum of position "eigenstates" - simpler wavefunctions which correspond to the particle(s) having definite positions. But to get momentum predictions, you break it down into a different sum, a sum of momentum eigenstates. (In terms of waveforms, the difference between a position eigenstate and a momentum eigenstate is the difference between a waveform which is peaked at one point and which is zero everywhere else - that's a position eigenstate - and a waveform which extends everywhere and consists of waves of constant wavelength - that's a momentum eigenstate.)
The more general rule, is that to get predictions for some observable property, you break the wavefunction into a sum of eigenstates or eigenfunctions for that particular observable property. The eigenstate is a state where that property definitely has a particular value - with 100% probability. A sum of eigenstates with different eigenvalues corresponds to some probability for one value, and some probability for the other value. And there are definite rules or patterns for what sort of waveforms / functions / quantum states, are the eigenstates for a particular observable property like position, momentum, energy, etc.
The essence of the many worlds approach, is to say that the wavefunction is a real thing, the fundamental thing in nature, and the eigenstates that it contains, are the many worlds. But there are multiple ways to decompose a wavefunction; which one, if any, is the correct one? Common sense would probably favor the position eigenstates, because they most resemble the world of common sense. But the preference among many-world believers is to say that no particular choice of eigenstates is preferred. They think they can do without a "preferred basis" (as it is called), just as relativity does without an objective universal time coordinate.
However, this has never been turned into a coherent ontology or picture of reality. So at bottom, many worlds just consists of orthodox quantum mechanics, plus rhetoric and vague intuitions about multiple worlds. It does not consist of a mathematically exact model in which there are definite worlds that interact in an exactly specified way. In the last few years, that sort of theory has finally been defined mathematically, under the name "many interacting worlds" (MIW). But it is a modification of quantum mechanics, a modification made precisely so as to specify which eigenstates are the worlds, and to have definite laws of inter-world interaction. Back when Deutsch wrote The Fabric of Reality, no such theory existed - his remarks about the double slit experiment being explained by the interaction of photons in our world with "shadow photons" in other worlds are pure rhetoric.
So it's a little hard to answer your question within the MWI framework, because that framework only exists in a vague way. Someone working on MIW might be able to answer it in exact terms.
