Mr. Laser Beam wrote:
Am I correct in assuming that the prime universe DTI has no way of knowing of the existence of the Abramstimeline or the time travel that created it?
That's correct. As far as they know, Spock and Nero just fell into a black hole and were crushed.
The Abramsverse DTI, on the other hand....
...doesn't exist, at least not yet. The Primeverse DTI was founded in 2270 in response to Kirk's time-travel experiences in TOS. The "current" timeframe of the Abramsverse is 2258 and Kirk has just gotten his command.
Maybe the prime Dulmur and Lucsly don't know about it, but what about Daniels? Within about 24 hours of seeing the latest ST film, I had already imagined a scenario in which Daniels pulls Spock aside (the way he frequently pulled Archer aside), informs him that the hypernova that will had (time travel plays havoc with tenses!) destroyed Romulus will had been the first shot in a 24th century front of the Temporal Cold War, and asks him to undertake a mission to essentially wipe the Abramsverse out of existence and reinstate the Prime Universe.
Nothing happened to the Prime Universe. It's still there, coexisting with the Abramsverse. So there's no reason the Abramsverse can't continue to exist. The reason Spock Prime wasn't already trying to fix the timeline in the movie is because he knew there was nothing to fix, nothing to change -- that the Abramsverse hadn't replaced or erased his own history, simply branched off from it.
Besides, what I said above still applies -- we don't know if Daniels's agency would even have any awareness of that other timeline's creation. There are so many different timelines that it's probably hard to keep track of them all even with 31st-century technology. And as long as a timeline doesn't pose a threat to the existence of a different one, there's no reason to get involved.
Also, I really doubt that Daniels himself personally deals with every
time-travel issue arising across all of time and space. He's just one person, after all. And he made it pretty clear in "Shockwave" that he's not the top of the totem pole, just a team member following orders from higher up. Just because he's the only guy we've seen doesn't mean he's the only guy there is. That's part of why I created Jena Noi, a different member of the same agency, in Watching the Clock
. I figured that Daniels was assigned specifically to the mid-22nd century in this vicinity of the galaxy, while other agents would be assigned to other timeframes and regions.