No, absolutely nothing in the movie definitively establishes what universe/timeline/quantum reality elder Spock comes from.
Except for his character's name. The credits to a movie show the name of an actor and the
in universe name of the character he or she plays.
(preemptive response): It does not matter if no one in the movie
called him "Spock Prime." The credits at the end of the movie unambiguously identify the character as "Spock Prime." There is absolutely only one thing that this means and that is that the character is from the "prime" timeline.
Because of how easily it's argued. It's JJ, Bob Orci, etc who decided to not only accept TNG "Parallels" and the existence of an infinite number of quantum realities/timelines/universes, but introduce the idea that all time travel does is create other, new parallel, quantum realities. Does that mean that each of the dozens of time travel events in TOS-TNG-DS9-VOY-ENT-Movies created a new parallel, alternate quantum reality? Yes. That's not my pain in the ass self saying that, that's what they are saying.
That's exactly what Data explained in
Parallels.
So, in the vicinity of Klingon space, on Stardate 2233.04, a billion different things could have happened. We know for a fact that one of those billions of different possibilities, no matter how extremely unlikely, was the arrival of the Narada from 2387. That happened in one quantum reality. It didn't happen in another.
In other words,
yes, based on the established, canon, in-universe science of Star Trek (science as articulated by an in-universe character who is qualified to speak of such things), every single solitary arrival of someone from the future created an alternate timeline at the point they arrived. Kirk, Spock, and McCoy arrived back from the Guardian of Forever in an ever so slightly different quantum reality -- one that branched off when a drugged up future country doctor arrived and his weird friends came back to retrieve him.
On April 4th, 2063, an alternate timeline branched off at the point that Borg arrived, leading to the alternate reality where the Borg had assimilated Earth, as viewed from the Enterprise as they were protected by the time vortex. Yet another alternate timeline branched off when the Enterprise arrived in 2063 and destroyed the sphere. All of the subsequent events in the movie led to the Enterprise returning to Stardate 50893.5 in an ever so slightly different reality from the one they started in.
(preemptive response): I did not just say that Data said any of that. I said it was based on the science that he articulated.
LOL! So which Spock is this elder Spock? What "quantum reality' is he from? What alternate/parallel universe? We have no way of knowing. The onscreen evidence is not conclusive one way or another.
The credits of every movie identify the out of universe actor and the
in-universe on screen character they portray. Leonard Nimoy played the one listed as "Spock Prime". Prime means exactly one thing in this context.