Agreed. It’s just that obviously the timeline didn’t divert at the moment of James T. Kirk’s birth; everything’s up in the air as to what the next movie(s) might show.
What did Spock…and which one…say about an alternate time line?
From IMDb:
Spock: You are assuming that Nero knows how events are predicted to unfold. The contrary - Nero’s very presence - has altered the flow of history, beginning with the attack on the USS Kelvin, culminating in the events of today, thereby creating an entire new chain of incidents that cannot be anticipated by either party.
Uhura: An alternate reality.
Spock: Precisely. Whatever our lives might have been if the time continuum was disrupted - our destinies have changed.
I assume this is Quinto speaking. I don’t remember almost two weeks later.
Yes, but Spock thinks that the moment of divergence was the Narada’s attack on the Kelvin. Because of other instances of time travel, however, that divergence point altered later time travel instances which thereby retroactively (preactively? man, I hate time travel episodes) moved the divergence point earlier.
Which really messes up the continuity. “Enterprise” was supposed to be in-continuity for this timeline, at least going by the throwaway line about Admiral Archer and his dog. However, time travel screwing with the divergence point means that “Enterprise” continuity was also altered in this timeline.
And it’s not clear that the writers realized that effect was going to follow from their plot.
edit: and, yes, that was the Quinto Spock. Spock Prime didn’t have any scenes with Uhura.
Applying Occam’s razor, and given that Spock’s explanation was intended for us, I would say that the time lines split at the attack on the Kelvin and Kirk’s father dying.
Yeah, I agree that this series shouldn’t just serve to update old Trek ideas. I really don’t see how the Khan story can be improved upon, so I’d really they rather just leave that one as it is.
That said, I can’t be the only one who wants to see some big-screen Gorn.
“Time travel! Ever since my first day on the job as a Starfleet captain, I swore I’d never let myself get caught in one of these godforsaken paradoxes. The future is the past, the past is the future. It all gives me a headache… My advice in making sense of temporal paradoxes is simple - don’t even try!” - Capt. Kathryn Janeway
Heck, Trek has always been pretty casual about its continuity. An appearance by newKhan wouldn’t be a huge problem in itself, except it would display an utter lack of (and indeed disinterest in) anything approaching originality.
Spock’s explanation was intended for the audience, in general, but not specifically for that small fraction of the audience who would argue about continuity and alternate timelines.
But if we’re going to be applying Occam’s razor, I’d say the way it cuts it looks as though the divergence were before the Kelvin incident. Since from what we know of TOS, Kirk, Uhura, Sulu, Checkov, and McCoy were not of ages that they would have been in the Academy together. In particular, Checkov’s birth may have moved up, and McCoy’s moved back, making them all closer in age. (although, McCoy being a doctor may skew his age off the others at the Academy.)
And they really need to retcon continuity before the Kelvin incident. TOS continuity had the Eugenics Wars occurring in 1990. That may or may not have been whacked by the Temporal Cold War in “Enterprise”, but it’s all a muddle since the end of that apparently retconned most if not all of the Temporal Cold War’s effects.
Or, quite possibly, you’re overthinking things and they wanted a plot device to get them out of the corner they managed to paint themselves into over the last 40 years.
That would be the Occam’s razor arguement. 
But what if the impact of the other places where there was interference in the Alpha timeline? Would the Enterprise D be around to return to the point of First Contact? Would they need to, since the Borg only went back because of Picard? Is Spock Alpha going to tell Spock Beta about the Borg?
Thus it is somewhat reasonable to say the timelines diverge even before the attack.
I think a red matter black hole doesn’t just send you through time & space, it also sends you to an alternate reality time & space. So, there’s no continuity problem. Spock prime is now in a completely different reality, complete with an alternate history that can be as different as the writers need it to be. The only thing that’s changed for this reality is its future that might have been, but now isn’t.
I’d rather they explore strange new worlds, seek out new life and new civilizations, and boldly go where no man has gone before. Fat chance of that, though.
See, that’s a problem I have with Trek movies in general. Absent the hour-long weekly format, they all turn into Enterprise vs. some space villain, which jettisons most of the strengths of the series.
I can forgive that in this movie. Since we had to be introduced to all the characters, it’s basically the pilot. But I hope that by the next movie we’re actually seeing the Enterprise as an exploration vessel so that we can see something new.
Also, please no Borg.
Unless these guys are merely ignoring that, using the “different timeline” as a poetic license to change whatever they wish. 
Re: Kirk & company being Academy classmates:
I don’t have a problem with Kirk being in the same Academy class, or close to it, with Uhura. 60s!Kirk and 60s!Uhura are about the same age. Even in the original series he was young for a captain–just not RIDICULOUSLY young–while she was of average age for a lieutenant. But then, she wasn’t as driven to make captain’s rank either.
Nitpick: Enterprise-E.
+1.
When the movie ended on the reading of that line, the audience cheered - at least in part in the hope that future sequels would have the freedom & strangeness of TOS, and not more dreary space-opera politics.
Kirk, Sulu, and Uhura could have attended the Academy around the same time (their respective non-canon birthdates are given as 2233, 2237, and 2239, but Shatner, Takei, and Nichols all looked to be roughly the same age), while McCoy was implied to already be a doctor that was joining Starfleet to get away, and Scotty and Spock are already officers.
The only outlier in all of this is Chekov, and he’s 17 while people upthread are saying Kirk was 25 so even that fits since we don’t have Prime birthdates to play off of.
From startrek.com:
Full Name: James Tiberius Kirk
Date of birth: March 22, 2233
Place of birth: Riverside, Iowa, Earth
Education: Starfleet Academy, 2250-2254
Full Name: Spock (lineal Vulcan name unpronounceable)
Year of birth: 2230
Place of birth: Shi’Kahr, Vulcan
Parents: Ambassador Sarek and his wife Amanda Grayson
Education: Starfleet Academy, 2249-53
Full Name: Leonard H. McCoy, M.D.
Year of birth: 2227
Parents: Mr. and Mrs. David McCoy
Education: University of Mississippi, 2245-49; medical school, 2249-53
STARFLEET HISTORICAL FILE: Scott, Montgomery “Scotty”
Year of birth: 2222
Education: Starfleet Academy, 2240-44
Full Name: Pavel Andreievich Chekov
Serial number: 656-5827B
Year of birth: 2245
Education: Starfleet Academy, 2263-67
STARFLEET HISTORICAL FILE: Uhura
Date of birth: 2239
Place of birth: United States of Africa, Earth
Parents: Mother, M’Umbha
Education: Starfleet Academy, 2257-61
STARFLEET HISTORICAL FILE: Sulu, Hikaru
Mid-level Biography Brief Mode
Rank: Captain
Date of birth: 2237
Place of birth: San Francisco, Earth
Education: Starfleet Academy, 2255-59