I've read where spacetime was big banged from a singularity that came from a quantum fluctuation in the quantum vacuum. But I've also read that the quantum vacuum itself assumes spacetime, So which is correct?
The fact is:
nobody knows anything about what happened prior to about $10^{-43}$ seconds after the big bang. Therefore, any speculations about singularities or universes popping out of quantum vacuums are just that: speculations.
As others have said, some people have postulated the existence of a multiverse in which there is some kind of thing - call it a "quantum vacuum" if you like - that can (somehow!) spawn universes. Maybe there is such a thing; maybe there isn't. I'm not currently aware of any proposed experiments or tests that could possibly decide the matter one way or another, but maybe there are some proposals.
The term "quantum vacuum", when applied
inside our current universe, just refers to whatever the default background state of spacetime looks like at the quantum level. The Standard Model of particle physics assumes the existence of various types of fields. It describes all known particles as excitations of the various fields.
Under suitable conditions, new particles can be created out of the "quantum vacuum" and 'old' particles can disappear back into the vacuum.
Quantum field theories assume the existence of spacetime. They are theories of the fields and particles that exist within spacetime. They do not attempt to explain where the space and time come from in the first place.