The Kelvin timeline doesn't need to be fixed, because it's a parallel universe coexisting alongside the Prime universe. Indeed, DSC makes it quite clear that it still existed up until at least its 24th century, as Yor came from that timeline.
The entire point of the Abrams films was to establish a changed timeline from 2233 onwards so that they could tell their own stories without having to be restrained by 'canon.' What would be the point of Spock going back in time to some other pre-existing timeline? If he was going to do that, then there wouldn't have been a need for the time travel at all.
There has never been consistency with time travel in Star Trek.
There have been other universes (Mirror Mirror, Parallels), and there have been time travel that changes the fabric of their own universe, which must be fixed at the end (First Contact, City on the Edge of Forever, Endgame, etc).
So if we go with what Discovery has implied / stated, then The Kelvinverse was always a pre-existing alternate universe, a pre-existing physical space, not a time travel rewrite, and Spock both time traveled and tunneled into an alternate universe. I'm fine with that.
There has never been a time that time travel in one universe has spawned a co-existing universe, it has always been a timeline rewrite.