Logan was brainwashed and programmed to become a killing machine by this timeline's version of the Weapon X program. This includes the repression of personality and memories, to make him a more pliable weapon. The helmet, electronics, and chemicals (tubes in his stomach) put him in a Berserker mode, with the helmet causing him to hallucinate as Stryker and the doctors want him to. It's lifted wholesale from the original Weapon X story arc by Barry Windsor-Smith in "Marvel Comics Presents #72-84 Weapon X", unlike the butchered version in the Origins film.
In the first few pages into Logan’s abduction, we see that he is constantly being fed tranquilizers and other mind-dampening drugs. The reader is informed that the scientists have chemically and psychologically stripped Logan of his humanity and have reduced him to an animal. This is a theme seen through Wolverine’s storylines; the idea that he is more of a raging animal than a rational person. Windsor-Smith provides an antagonist that readers can truly hate in Logan’s defense. Thorton pulls no punches in Logan’s treatment. He has Logan stabbed with tubes and needles, turning him into a mutant pincushion.
In this timeline, at this point of 1983, Wolverine has never met Jean or Cyclops before. Jean, using her powers, unlocks some of Wolverine's mind, allowing him to return to the man inside the beast.
[Jean Mentally to Logan] "Logan".
[Wolverine removes his plugs, leaves]
Scott: What did you do to him?
Jean: I found a piece of his past and gave it back to him. Just a few memories I could reach.
Scott: I hope that's the last we'd seen of that guy. [Rimshot]
In the original timeline, they first meet in 2000, when Jean is already an adult teacher at Xavier's school.
The memories she unlocks are the ones Wolverine loses of his past before the Weapon X program. The same ones that Jean and Xavier attempt to help him remember in the original timeline in X1-X3. The same ones that he lost because of the adamantium bullet in Origins. Not memories that he had from the time travel in DOFP.
The biggest problem is DOFP, and it's "good ending". In DOFP, when Wolverine's mind is sent to the past, it only stays there as long as Kitty Pryde/Rogue can keep him there. Once she lets go, the time travel events are set, and Wolverine's mind returns. As he says at the very end of DOFP to Xavier:
Wolverine: History? Actually, I could use some help with that.
Professor X: Help with what?
Wolverine: Well, pretty much everything after 1973. I think the history I know is a little different.
[the Professor gives him a knowing look]
Professor X: Welcome back.
Wolverine: It's good to see you, Charles. It's good to see everyone.
Professor X: Well...I had a promise to keep. You and I have a lot of catching up to do.
Professor X: What's the last thing you remember?
This means the Wolverine in 1973 returns to his original memories. He keeps nothing. But the Wolverine in the "good ending" of 2035 suddenly forgets everything in the new timeline, and remembers the old timeline.
In any case, that means the Wolverine in 1983, in Apocalypse, has no memory of the old timeline, of meeting Jean in X1, the year 2000. He's completely unaffected by the time travel.