This sort of makes my point. When Biff took the sports book back to his past self in 1955 and his past self used it to get rich, then the timeline changed. Marty went back to 1985 and his reality had been altered! He was not in an alternate universe, or alternate reality witn ANOTHER Marty somewhere out there living an untouched life! There was only one Marty in his changed reality.
When he went back to 1955 and re-took the sports book, it changed the timeline, or his present, back to what it sould have been.
What I am saying is that the TOS crew is in the same position as this. Their future, or Prime Spock's 'present' has been changed. And just as Marty is the only one whe remembered what it had been, becuase he was outside of the bubble when the change happened, so is Spock Prime.
Now, If Spock Prime were to go back further into time, and be there when Nero showed up, and destroyed his ship, then the alternate reality, alternate timeline would revert back to what he had lived, and the changes would never have taken place.
But since Spock Prime does not have a delorian and seems to have forgotten the slingshot effect around a sun, we are now stuck with the altered reality that Nero set into place.
There is no 'other' TOS crew living the life as Spock Prime remembers. He was outside the buddle and Nu-Spock will have a completely different set of memories than Spock Prime does whe he grows up!