The Major Star Trek Time Lines:
Time Line A:
The Original Series Season's 1-3 - And it's 6 Films.
The Next Generation Season's 1-7 - And Generations
Deep Space Nine Season's 1-4
Deep Space Nine Season 5: "Apocalypse Rising" to "Blaze of Glory"
Voyager Season's 1-2
Voyager Season 3: "Basics Part ll" to "Distant Origin"
Time Line B:
(Prime Time: Nearly Identical But Slightly Different)
Deep Space Nine Season 5: "Empok Nor" to "Call to Arms"
Deep Space Nine Season's 6-7
Voyager Season 3: "Displaced" to "Scorpion Part l"
Voyager Season's 4-7
Time Line C:
(Separate Alternate Time Line)
Star Trek (2009)
Time Line D:
(Unexplained First Contact / Temporal Cold War Time Line)
Enterprise Season's 1-4
Time Line E:
(Unexplained TOS time line)
The Animated Series Season's 1-2
In other words:
Old Spock comes from Time Line B. A time line that is nearly identical to Time Line A (The Prime Time Line), but slightly different.