Another thing to consider is that Spock has been out of Starfleet for at least 75 years (if not longer), and as an ambassador is probably used to dealing with different levels of technology (Federation and non-Federation). He simply adapts to what he has, IMO.
I also think that the tech in nuTrek isn't that terribly different from the original universe and timeframe he left. It may be less powerful, but otherwise a lot of the basic stuff is still there and he can modify it to suit his needs if necessary.
Free your mind, and the rest will follow.