'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.
Also, old Spock watching Vulcan get destroyed looses a bit of its punch since we know that his planet Vulcan still lives in another timeline. But Nero and old Spock himself as shown in the movie sure do think it is the Vulcan from the other time line.