Because the dark-matter wave that hit him and Jesse wasn't just any old dark matter, it was from the experiment that recreated the accident that gave Barry his speed. Indeed, I got the impression that it was, in some way, Barry himself -- that when he vanished into the Speed Force, he passed through them along the way. At least, it was the same dark-matter surge that gave speed to both Barry and Jesse, so presumably it had some kind of a Speed Force component to it, and thus it's logical that the third person exposed to the same surge could also get speed from it.