The first J.J. Abrams
Star Trek movie establishes that this would be okay: old Spock (Leonard Nimoy) recognizes young Spock (Zachary Quinto) as himself. Same with old Spock laying eyes on Kirk (Chris Pine) and Scotty (Simon Pegg) and “seeing” the Scotty and Kirk he knew in the past. It’s one of those things that requires the audiences to give the reboot movies a break, but it does seem to the intent. Two actors: same character.
To put it another way, nobody thinks Saavik in
Star Trek III is from a different universe than Saavik from
Star Trek II even though one was played by Robin Curtis and one was played by Kirstie Alley. Similarly, no one who is a fan of the
Marvel movies would claim that the first
Iron Man is in a different universe than the other movies even though Roadie is played by Terrence Howard intially, and then later, by Don Cheadle.