There's nothing in the movie that says it has to be "our" Old Spock. It's an Old Spock. There's probably billions of them in the multiverse. With the timeline branching all over the place, both spontaneously and through deliberate action, there's probably more Spocks than you could count. One data point is hardly enough to draw a definite conclusion from. It's not like we saw the Enterprise-E and crew, looking pretty much like we last saw them. The movie is vague enough that pretty much any explanation could work. It's not like we're going to see the old universe again anytime soon.