How'd he fight himself then?
Let me explain this a different way.
There is no Jay Garrick that's separate from Zoom. "Jay" was never anything other than an identity that Zolomon made up when he broke out of prison. The "Jay Garrick" that everybody (Wells, Team Flash, people on Earth-2, etc.) knew was always just Hunter Zolomon pretending to be a hero. No time travel involved. One day the portal opens to Earth-2 and Zolomon finds out there's another Flash there. He decides to steal his speed an uses his "hero" identity Jay Garrick to infiltrate the team and earn their trust.
Later on in the season, Team Flash starts closing the portals between Earths. Since there's not that many portals for him to use now, he can't easily jump between Earth's without anybody noticing. So he makes a quick trip to, say, yesterday and grabs himself from then, and has that version of himself stay on Earth-2 and act as Jay so that Team Flash doesn't get suspicious about his absence. And he eventually kills that version of himself.
You get what I'm saying? Jay Garrick was always Zoom. The time remnant was just a recent thing he thought of to throw team Flash off, not something he'd been doing before then.