'09 Old Spock is the same Spock we first met in 'The Cage.' What he mistook for mere time travel via Nero's red matter was in fact them crossing universes - from the Prime Universe over to the Abramsverse 150-something years in the past.
I agree with you but the movie is as clear as mudd about that. Young Kirk and young Spock et al. sure do think that Old Spock and Nero are from their future
. But they're not.
Let's not get carried away here. Spock and Nero time-traveled from their era to their past. The timelines diverged because of their incursion. Whether there are parallel timelines is irrelevant. They can no more travel to "their" proper past than you can travel to the universe in which you turned right when instead you turned left.