This may be a partial answer as I haven't seen the movie, but I've been reading about it in anticipation of going. From Wikipedia we learn (emphasis mine):
At a tense meeting with IRS inspector Deirdre Beaubeirdre, Waymond's body is taken over by Alpha-Waymond, a version of Waymond from the "Alphaverse." Alpha-Waymond explains to Evelyn that many parallel universes exist because every life choice creates a new alternative universe. The Alphaverse, led by the late Alpha-Evelyn, developed "verse-jumping" technology, which enables people to access the skills, memories, and bodies of their parallel-universe selves by performing bizarre actions that are statistically unlikely. The multiverse is now threatened by Jobu Tupaki, the Alphaverse version of Joy, whose mind was splintered after Alpha-Evelyn pushed her to extensively verse-jump. Jobu now experiences all universes at once and can verse-jump and manipulate matter at will.
What we learn from this is that, I'm assuming, the word "universe" isn't used throughout the movie save in the one instance you mention. At some time the idea of the multiverse was explained, including the fact that Joy from the Alphaverse became Jobu Tupaki.
What Wikipedia didn't explain was how the producers structured indexing for the multiverse. It's incredibly important that you keep in mind that there's a better than average chance that they didn't. A reference like "4,655th thetaverse" is one of those phrases that adds flavor and depth to the story. It begs questions like these:
There's an Alphaverse and a Thetaverse. There's 8 letters in the Greek alphabet between and including Alpha and Theta. Are there 8 "primary" universes? Or is it more like mathematics where we tend to only have Alpha, Beta, Gamma, Theta, and Epsilon?
What's the difference between primary and secondary universes? Why are there 4,655 Theta-type universes?
My thanks to @GalacticNinja, who has seen the movie, for pointing out that there is but one Alphaverse, the discovery of multiverse travel was developed.
The problem is that writers, directors, and producers want you to ask questions like that but don't necessarily want them answered. At least not yet. They want viewers to get jazzed by the possibilities of the world they've built — but they don't want so many answers given away (if any...) that interest is lot. In short, your wonder is more valuable to movie companies than your satisfaction. (Funny to think about....)
What I like about this aspect of their worldbuilding is the sense of promise that Jobu Tupaki, who can experience all universes at once, has apparently come up with an indexing system to keep it all straight — despite having a splintered and presumably damaged mind. In other words, you might not be able to trust the indexing system even if it's revealed. It was created by someone who's insane. The desire for order blossoming from chaos is very germane to human psychology, so that bit of worldbuilding sets up a stressor — the hope of order even though it's likely false. Cheers to the writers!
Disclaimer: I could be wrong in that somebody may have described the differences between primary and secondary universes. But as new as the movie is, I'm prepared to doubt that possibility.