^Except in the movie they never mention hopping timelines and universes at all. They say Nero and Spock went back in time, and that by altering events in the past they created an alternate reality.
Okay I'll attempt to reconcile what the writers said they wanted and obviously intended with what they had the characters say and do on screen, even though the real answer is that the writers weren't terribly precise about any of this, not wanting to stop the movie dead for a half-hour lecture on the nature of space and time.

Instead they handled the whole thing the only way they could, in about ten words, and considering that I and many other people managed to get the picture based on that, I'd say they did pretty good with their choice of ten words.
Spock & Nero changed a timeline, but clearly not their own timeline, since the writers have gone to great lengths to assure fans that the original Prime Universe was unaffected by the movie.
So that means that Spock & Nero created some universe that didn't previously exist by their actions. Uh. It must have previously existed, or else how was George Kirk & the redoubtable Robau alive at that point? Plus they had all kinds of history that they remember.
So did Spock & Nero in effect clone a new universe, seamlessly, so nobody noticed, like a new tree branch budding off an existing one? Sure, why not. The upshot is that nobody noticed that they suddenly veered into a new universe, even if they knew, there's nothing they can do about it, the original branch is unaffected and the new branch is where the action is now.
I don't think this is what "really" happened because
Star Trek has been living in multiverse land ever since Mirror, Mirror. Multiverse theory holds that there is an infinite number of parallel universes. The other option is that there is one universe, end of story. So if you know of two universes, then you've hopped into multiverse-land. Why should there just be two universes (and now three?) Why would it stop at that number? It doesn't make sense intuitively. What makes sense is one, or infinity.
The one and only reason TOS/TNG etc weren't "erased" is because the writers retconned how Star Trek time travel works to the multiverse model (which it has used before, just not as frequently as the single-changable-timeline one).
They didn't retcon it because they established that there's at least one other reality in Mirror, Mirror. That was the big seismic change. Additional realities should come as no surprise. I'd be far more surprised if there were
only two realities.
If Kirk & the gang had a transporter accident that took them to the MU in the 22nd C, that would have been perfectly legit as a storyline, and anything they did in that story would not have had an impact on their own timeline, since they are in a different reality that does not intersect with their own. That sort of time travel has been possible in
Star Trek for decades now, but writers have not chosen taken advantage of that, instead sticking (generally) to time travel within the characters' own reality.
So we're talking about two separate types of time travel which have entirely different consequences. Time travel within your own timeline has not been dispensed with either in the Prime U or Abrams U, and stories could be written in the future using that system.
How the MU came into being is another issue - I like the notion that Edith Keeler didn't die and set in motion a disastrous chain of events - but that assumes there was a separate MU reality all along, because in the Prime U timeline, she did die, so whose timeline was it where she survived? Someone else's.
So if the MU always existed, then there are realities that "always exist" in parallel to the Prime U, and why shouldn't the Abrams U follow this pattern as well? Maybe the Abrams U "always existed" as a near-perfect clone of the Prime U, and its trajectory was altered by the introduction of Spock and Nero.
If there's an infinite number of realities, anything that could happen must happen in one of them. Spock & Nero had to do what they did in some reality or other, so why shouldn't it happen in the reality where the cameras are pointed at for our movie?
She actually said "an alternate reality".
Oh, thanks. So Orci & Kurtzman
were clear. How can an alternate reality be interpeted as anything but, well, an alternate reality? It's a different universe, case closed. The only question remaining is whether the different reality happened through a tree branch budding, or more like the MU, and was always there, but that's a philosophical question that has no bearing on how the story goes or will go in the future.
Technically speaking, there was nothing in this movie aside from that throwaway line from Uhura that made any suggestion whatsoever that the TOS/TNG timeline still exists.
There was no reason to believe that anything untoward had happened to the Prime U, either. Practically speaking it will remain dormant until such time as
Star Trek writers decide it would be fun to return to it. Then it will suddenly spring back into being unharmed and I wouldn't be surprised if these future writers decide that Romulus actually wasn't destroyed after all, which of course will lead to furious fan speculation that this is a different universe altogether...
Or we could all choose to believe that the universe Old Spock came from wasn't the Prime Universe. It could have been some heretofore unknown fourth reality. There are an infinite number of Spocks bopping around the multiverse, so whose to say who that guy was?!?
Question: If we accept that the Narada affected the TOS timeline, why can't we accept that the TCW/Xindi incidents in ENT affected the pre-TOS timeline?...
a) The Narada did not affect the TOS timeline in the Prime U and for all we know, the Narada was "supposed" to affect the Abrams U in exactly the way it did.
b) The TCW was so badly written that it's anybody's guess what happened.