Usually when people say something is untestable they don't mean like the Higgs Boson. It was testable, they just needed the proper tools. This was always known and was being actively worked towards. An untestable theory is one that cannot be tested regardless of the tools due to the nature of the theory. Multiverse is an example of an untestable theory. There is no way we know of to actually prove or disprove it. And its fair to question their legitimacy as theories. As testing a hypothesis is the core action of the scientific method, it logically follows that anything untestable is fundamentally not science and therefore not a theory.
In this case I think multiverse is both. Testability and falsifiability are closely related. But its possible to make a testable statement that can't be falsified in most examples I can think of the test can't be exhaustive.
A theory can be untestable but also falsifiable. For example, while the multiverse theory/interpretation may be untestable, it could be immediately falsified if QM were falsified.
Popper's falsifiability criterion was more aimed at theories like Marxism, where it seemed that within the theory there was always something available to account for an exception or challenge.
