Pure fan service. Would the writers have written a scene in which he contacts Prime-Spock about a bad guy called Nebulon or somthing?
Quinto's Spock may very well have contacted Nimoy's Spock about Nebulon in-universe, but since Prime Spock would have no info we (the audience) would not see that interaction as it would not be relevant.
Well, he probably wouldn't bother Spock Prime about every little thing, because as large as the galaxy is, the chances they shared exactly the same experiences and met all the same people is very small.
Yet, Spock must have in mind the theory alluded to in ST09 that life events in both universes are as similar as each will allow given their differences. (The same paths keep crossing -- certain people are destined to be thrown together.) Therefore, Spock may have believed that in a case involving a threat as big as Khan, there would be a fair probability that Spock Prime and Kirk Prime came across him somehow, and were equally if not similarly imperiled. So, why not take a chance and pick Spock Prime's brain about what they did?