I know I'm late to the party, but I couldn't help but notice that this interesting question hadn't been answered (here, at least). So here it is: as far as I know, B 'splits' immediately, but this in an unphysical question.

In MWI we would have observers A and B, who could observe Aup or Adown and Bup or Bdown (and start in |Aunknown> and |Bunknown> before measuring) respectively. If we write |PAup> and |PAdown> for the wavefunctions corresponding to the particle near observer A being in the up resp. down states, and introduce similar notation for the particle near observer B, then the initial configuration is:

|Aunkown> * |Bunknown> * (|PAup> * |PBdown> - |PAdown> * |PBup>) / \sqrt(2)

Now if we let person A measure the particle the complete wavefunction changes to:

|Bunknown> * (|Aup> * |PAup> * |PBdown> - |Adown> * |PAdown> * |PBup>) / \sqrt(2)

Important is that this is a local change to the wavefunction, what happened here is merely that A measured the particle near A. Since observer A is a macroscopic object we would expect the two branches of the wavefunction above (separated by the minus sign) to be quite far apart in configuration space, so the worlds have definitely split here. But B still isn't correlated to any particular branch: from the point of A, person B is now in a superposition. In particular observer B doesn't notice anything from this splitting - as we would expect (splitting being a local process and observers A and B being far apart). This is also why I called the question as to when B splits 'unphysical' above, since it is a property known only locally at A, and in fact the answer to this question wouldn't change any of B's anticipations.

This might seem a lot like RQM, and that is because RQM happens to get the answer to this question right. The problem with RQM (at least, the problem I ran into while reading the paper) was that the author claims that measurements are ontologically fundamental, and wavefunctions are only a mathematical tool. This seems to confuse the map with the territory: if wavefunctions are only part of our maps, what are they maps of? Also if wavefunctions aren't part of the territory an explanation is needed for the observation that different observers can get the same results when measuring a system, i.e. an explanation is needed for the fact that all observations are consistent. It seems unnecessarily complicated to demand that wavefunctions aren't real, and then separately explain why all observations are consistent as they would have been if the wavefunction were real.

I think this is what Eliezer might have meant with

As far as I can tell, the only possible coherent state of affairs corresponding to RQM - the only reality in which you can embed these systems relating to each other - is MWI

RQM seems to assert precisely what MWI asserts, except that it denies the existence of objective reality, and then needs a completely new and different explanation for the consistency between measurements by different observers. I found the insults hurled at RQM by Eliezer disrespectful but, on close inspection, well-deserved. Denying reality doesn't seem like a good property for a theory of physics to have.