Although Tegmark incidentally endorses MWI, Tegmark's MUH does not entail MWI. Yes, if there's a model of MWI, then some world follows MWI; but our world can be a part of a MUH ensemble without being in an MWI-bound region of the ensemble. We may be in a Bohmian portion of the ensemble.

Tegmark does seem to think MWI provides some evidence for MUH (which would mean that MUH predicts MWI over BM), but I think the evidence is negligible at best. The reasons to think MWI is true barely overlap at all with the reasons to think MUH is. In fact, the failure of Ockham to resolve BM v. MW could well provide evidence against MUH; if MWI (say) turned out to be substantially more complex (in a way that gives it fewer models) and yet true, that would give strong anthropic evidence against MUH. MUH is more plausible if we live in the kind of world that should predominate in the habitable zone of an ensemble.