User blog comment:Crosaffcheg/Barry screwed up again/@comment-24042303-20170130180116/@comment-3221148-20170130180649

It's a paradox. Wellsobard still somehow existed, so that the Flash's memories and current, 2013-origin history would make sense.

The fact that Eobard exists in the new world is a paradox. On his twitter, Matt Lestcher said that there's "a CRAZY deadline" that forces Eobard to hunt for the Spear of Destiny (most likely, the Black Flash erasing him from timeline).

Matt also hinted that Eobard somehow got memories of his Wellsobard self after traveling through the Speed Force, so that he can be essentially the same person as at the time of his death. He also said that more info on Eobard's origins will be given to us in the "Legion of Doom" episode.