There are a number of different multiple Universe hypotheses.
It's important not to confuse them because they're not the same.
I've personally never liked the 'fine tuning' one mentioned.
The 'problem' is that many physical constants seem just right for matter and life to exist.
The 'Solution' is to propose a number of undetectable other Universes which have different constants.
I'm sorry but proposing an untestable hypothesis to explain an observation you don't like isn't what I understand as Science - it's what happens when you let a bunch of theorists go to the pub alone without an adult!
We don't understand how these constants got their values - it may be that there is an interalation between them and the probabilities of them being set at what they are is not as astronomical as they appear.
It may be that they are not actually constant but can change there have been some suggestions to this recently
http://phys.org/news202921592.html
As to the multiple worlds theory of Quantum Mechanics - again this is unprovable, it is a self-consistant 'interpretation' of QM which is to say it's one way of picturing the observations but not distinguishable from other interpretations.
This isn't actually quite the same as the many dimensions of String Theory. We're not talking seperate parallel worlds with seperate laws of physics and copies of the Universe here, we're talking other physical dimensions perhaps shrivveled up 'failed dimensions' remnants if the big bang only detectable on the very fine scale.
To me this sounds pertentially more plausible but again my problem with all of string theory (and many oth the other multi-worlds issues) is - 'call me when you have a testable hypothesis'.
But before we totally dismiss all of this remember that just a hundred years ago people thought the Universe was just what we now see as our Galaxy.
We keep finding the Universe is way bigger than we originally thought
But that's no reason for a magical creator