So, who is John Harrison?
Personally I think he is a character we have met before we has assumed a new identity for some reason or another. It could be that the new timeline has set his life in the direction where he ends up in Section 31 as Starfleet's version of James Bond. Or he could be listed as dead and works under an assumed name for one reason or another.
I'm still leaning towards the presumed dead Gary Mitchell--who may have had a long connection with Carol Marcus.
I do not however think it is Khan or any of his men. It would strain things for Khan to be found by someone else and then fake an identity to gain vengeance for something.