You're right on the money, but Thawne doesn't tell us where the fight took place. Was it Earth-38? Earth-1? The original Earth-1 timeline? Earth-X? Earth-C?

And we know that Thawne isn't the only one who can cross dimensional boundaries. Flash can do it, so can Cisco, Gypsy, Zoom, The Ray...and Supergirl. So did Reverse Flash travel to Earth-38? Or did Superman borrow Kara's dimension-hopping device and go to Earth-1?

Perhaps there's a reason both super-cousins turn up? The Crisis is on it's way, after all.