The point is that one cannot argue the multiverse idea passes from metaphysics to physics on the backs of scientific theories about cosmology and strings if the justifications one uses that multiverses are scientific do not invoke any of the empirical connections from those other subfields. Those subfields are what I might call "image spaces" for taking observational projections of reality (assuming this can even be done in string theory, I'll give them the benefit of the doubt), but multiverses don't inhabit those image spaces if one can discuss them independently of those image spaces. And if is to be its own image space, then it needs its own empirical projections, its own body of relevant predictions and data collections. One can't say it is a theory that piggybacks on cosmology or string theory and then say that the reason it is science has nothing to do with those other theories.
Exactly, it's a classic case of "having it both ways"-- multiverses are supposed to be the most natural interpretations of cosmological observations, yet they exist at distances that are beyond those very observations. His rhetorical dance seems to borrow support from the same observations he needs not be constrained by-- that's some trick.

Yes, I'm afraid his own words serve as refutation enough. How could someone as smart as Tegmark, with as much physics acumen as he has, not see the absurdity in claiming that "finite space" is experimentally unsupported, as though infinite space had experimental support? Also, wave function collapse is what you get if you don't make experimentally unsupported philosophical claims about the meaning of quantum mechanics (as Bohr well understood). And as for "ontological asymmetry", I have no idea what he means by that, but simply labeling something an "asymmetry" does not make it ad hoc--usually it is the assumption of a symmetry that is ad hoc!