In Terminator: Genisys :
Skynet gives John Connor new powers, by modifying him at cellular level.
But the new being retains all of his memories and all of his personality traits. But how does it make him its ally? Does he succumb to the power he receives and lose his mind? Does he see the Human and Machine alliance as a boon for humanity?
The movie explained Connor's conversion as insanity.
REESE: Skynet's made John into a Terminator.
POPS: Yes, Kyle Reese.
SARAH: They were trying to make a machine that could think like a man?
POPS: But the experiments failed. The human subjects went insane and died.
SARAH: Yeah, well, John's got the crazy part down.
John Connor never had a normal life. The looming spectre of Skynet dominated his existence from birth to the final battle where he thought he'd beaten the machines. Then Connor realizes that a) he hadn't won at all, b) he'd accomplished nothing, c) all his friends were dead and only a burnt husk of a world was left to show for it, d) he suffered an agonizing conversion into a machine himself. It wouldn't take much of a push for Connor to topple over into madness and see his lot firmly aligned with that of the machines. This, instead of continuing to side with humans in a demonstronably futile war.
It's true that our personality is largely shaped by our experiences, but that's not the same as saying that your memories are your personality. So just because someone has all of your knowledge or even your memories doesn't mean they'll think and behave exactly like you.
A simple example of this are your past selves. Your 16-year-old self had pretty much all of the memories that your 6-year-old self had, but did you behave exactly the same at age 16 as you did when you were 6? What about now? Do you have exactly the same desires/values/perspectives now as you did when you were 16? If not, then clearly someone can possess the same memories and even retain all superficial personality traits (language patterns, mannerisms, favorite foods, etc.) but still behave differently in more fundamental ways.
Another example of this are beta-blocker drugs that are used to treat PTSD. Beta-blockers don't erase memories of trauma, but when used during recall of traumatic memories, they can dull the emotional associations you have with the event, changing the way you perceive those memories in the future and thus alter how your behavior is affected by those same memories.
So I see no reason why the John Connor replicant can't have all of John Connor's knowledge and memories and be able to act like John Connor but still have his allegiance switched from the Resistance to Skynet.
Likewise, they could have just scanned Connor's brain for his knowledge/memories while the machine-phase matter ate and replaced his body, effectively killing him while creating a T-3000 that looked just like him and could behave like him using the scanned memories but was still programmed to work for Skynet.
Imagine I replaced one cell in your body with a microscopic machine that did the exact same function. Are you still you? What if it was 2 cells? Are you still you? At what point do you stop being you and be a machine instead?
Skynet replaced every one of Johns cells with a nanite. At which point Skynet had complete control over John, absorbing all of John's memories, his skills and knowledge. This created a terminator human hybrid.
