Oh geez, the "purist" is coming out. ahh damn you all for doing this to me..

..just kidding. But in Space Seed they mention that Kahn was one of the last tyranical leaders of earth in the 1990's. Is it me, or did they leave that part out.
I was very suprised to hear McCoy say that they cryo pods were "300 years old" - I'd have expected them to bump Khan's era up past our present. They went above and beyond to keep continuity with the old, IMO.
Maybe this Khan himself is from an alternate timeline from the one depicted in "Space Seed."
After all, in the "Voyager" episode "
Future's End," Henry Starling used future technology to become a wealthy inventor in the 20th century, and the Voyager crew traveled to 1996, which seemed perfectly pleasant with no signs of a Eugenics War going on.
So maybe Khan of this new movie is from that Henry Starling timeline, with a much different history from that of the Khan from the TOS timeline.
The timeline has been altered numerous times over the past three centuries, before Nero and Spock ever showed up to alter the timeline one more time.
Before the last Trek movie, this timeline has been visited by Janeway and Captain Braxton in the 20th century, the Borg and Picard in the 21st century, Daniels and his Temporal Cold War opponents in the 22nd century, and finally Nero and Spock in the 23rd century.
So even before Khan's birth, he was already in an alternate timeline created by Henry Starling using Captain Braxton's timeship technology. Nothing about his life would necessarily be the same as the Khan depicted in TOS before any of these alternate timelines started.
Perhaps when Spock Prime followed Nero into this new movie's timeline, it was not their own history they went to, but one of the many alternate timelines that were created over the past four centuries.
As seen in TNG's "Parallels," multiple timelines with divergent histories exist simultaneously, in addition to the Mirror Universe, all interconnected to each other at different points in time.