Currently the wiki has locked down Hunter Zolomon editing, which is a shame, because the article is currently all over the place regarding whether the Time Remnant was with us only for a day, or ever since the portal to Earth-1 opened. Thus, whether Hunter Zolomon became Zoom much later in the timeline and then traveled back in time to meet his Flash self and convince him to work together, OR whether the time travel is relevant only for getting a copy of Zoom, but both of them had the same memories.
Me, I think it's pretty obvious that Hunter pulled up a Time Remnant only after Barry decided to go to Earth-2. But, let's look at the dialogue from "Versus Zoom" again.
Joe West: Why the charade? Running around dressed like The Flash?
Hunter Zolomon: To give people hope, Detective.
Joe West: Hope?
Hunter Zolomon: So I could rip it away from them. It's so fun pretending to be a hero!
So, firstly, it doesn't seem like he became a hero, then a villain, then traveled back in time to pick up his hero self and work together. Zolomon became the Flash and Zoom at the same time, "to give people hope and to take it away from them". Interestingly, that he portrayed the Flash as a weaker, "cowardly" speedster, who was no match for Zoom.
The second dialogue, however, brings the confusion on whether the Time Remnant was only for a small period of time, or with Team Flash since the opening of the breaches.
Barry Allen: So this was your plan all along, huh?
Hunter Zolomon: Ever since the skies parted and showed me another world, with another speedster. Once I saw you, I came here, figured out what I had to do.
Iris West: How are you still alive? We saw you die.
Hunter Zolomon: You did.
Cisco Ramon: So what was that? A speed mirage?
Hunter Zolomon: [chuckles] Speed mirage? Uh, no. Even I'm not that fast. I knew that I couldn't be on two Earths at the same time, so I went back in time and, uh, met another version of myself.
Cisco Ramon: Your time remnant. Like the Reverse-Flash.
Hunter Zolomon: I also knew that the only way to make Barry become faster was if you all witnessed your old pal Jay die.
Iris West: When did you decide to do that?
Hunter Zolomon: Oh, once you closed all the breaches, went to Earth-2. Believe me, getting my time remnant to agree to me murdering him took a bit of convincing. But once he saw the... well, the genius in my plan, he was all for it.
So, here's the problem: Hunter says that he was planning his scheme "ever since the skies parted" to Barry, but "once you closed all the breaches, went to Earth-2" to Iris. In the same conversation. I think it's pretty obvious, that when he's answering Barry he's talking about his plan in general: the plan to go to another world, find another speedster and steal their speed, supposedly curing himself from the Velocity drug after effect. However, regarding the Time Remnant, he pulled him out of the timeline at the time of the Two Earths crisis, as he says to Iris. Actually, I think we can pinpoint the window where he time traveled on Earth-2, got his time remnant and brought him to Earth 1: the weird "nap time" moment during Escape from Earth-2. To remind it, after saving people from a falling building, "Jay" says he needs to take some rest, and leaves Caitlin and Iris alone, supposedly to sleep. Now, as soon as he leaves, the Geomancer enters S.T.A.R. Labs, proceeds to start an earthquake in the middle of the lab, hunts down the girls and ends up blasted by Caitlin. But as soon as his attack ends, "Jay" comes down, apologizing for coming too late. Wow. Nobody picked up on that when watching the episode? An earthquake happens in S.T.A.R. Labs, and "Jay" doesn't even hear it? Obviously, he didn't react to Geomancer because he wasn't around. I think that the "Jay" that apologizing for coming too late is a Time Remnant, as Zoom appears on Earth-2 exactly when this time window opens, while "Jay" helps Caitlin to regulate the breach. Finally, Hunter Zolomon appears to be in love with Caitlin, convinced that their love can continue despite the "Zoom" revelation: if it was only the Time Remnant who dated Caitlin on Earth-1, current Hunter wouldn't have cared about her at all.
One of the problems people noted about the Time Remnant explanation was the fact that if Zoom traveled BACK in time to get a disposable version of himself, rather than forward, surely he would die by killing himself? Well, there are different ways to handle this problem:
1) Because he changed the past version's way of thinking and actions, the past Hunter's actions wouldn't lead him to become the exact version of the time traveling Hunter that exists. This one's a bit hard to explain, but hear me out: if a time traveling version of yourself meets you and interacts with you, or even carries you forward in time, your actions and mind are obviously changed by this experience, and you might not end up doing the same and "keeping the time loop", which should basically diversify both you, and the time-traveling you as different individuals. NOTE: However, that means that "time remnant" is a misnomer, and Hunter just somehow evaded the self-killing paradox.
2) Speedforce acts as a "bunker" for speedsters, protecting them from whatever time changes occur at the moment. Since Zoom was (partially) in the speedforce when he killed "Jay", it means that he was protected from time paradoxes. NOTE: However, that means that "time remnant" is a misnomer, and Hunter just somehow evaded the self-killing paradox.
3) It's possible that Hunter travelled in time multiple times, creating an actual time remnant. Basically, instead of going into the past and convincing the past version of himself to die, he instead goes into the past, back to the future, again to the past, and arrives at the same moment as another time traveling version of himself (who is preserved by the speedforce / "timeforce" / w/e), explains: "Hey, that plan you just thought of? I am completing it right now, so don't travel back to the future, I'm gonna need you to die before Barry's eyes", after that just existing at the same time with the Time Remnant.
Finally, what is the "complication" Hunter spoke of to himself? I think it has nothing to do with his "death", but rather with the fact that he can't go back to Earth 1: his cover is blown and the Time Remnant ended up helping to close the last breach.