I mean, I think there’s several answers to this. Unfortunately, the movie only gives us the externality, we don’t know what Newt’s emotions are doing in any given moment, we really don’t even know when it’s really him or the Precursors masquerading as him, except with the “They’re in my head” line. 

– In the novelization, I hear they could control Newt’s emotions to some extent and direct his thoughts, so that up to the minute the plan went into motion, he still thought he was on the good guy side. 

– My theory about what’s happening in the movie, is that they didn’t actually control Newt from minute to minute as such, they just changed his central motivations. As in “If you wanted to destroy the world, how would you do it?” and then just let Newt go about it exactly as he would if that were something he actually wanted (hence his ability to showboat during the final battle and make sarcastic comments about Jaegers and stuff, that IS Newt, it’s Newt if he actually wanted to destroy the world, that’s exactly how he would go about doing it, they just made him want it) and the Drifts with Alice were to keep their programming running and keep him plugged in to their will, hence their regularity. In that version, I’d say they can usually just override him except when it was something so cognitively dissonant to him that he can tell it’s not something he wants, like hurting Hermann, which made him finally realize just how much he was being controlled. 

– In “The Only Way Out is Down” Newt is much more the hardware the Precursor software runs on, it’s his body, and they need him kinda conscious when they need info on our world or guidance on how to fake being him (basically he needs to be near the surface so they can read his memories), but whenever they want to override him because he didn’t want to do something, they’d just pushed him down into his subconscious. This was a deliberate authorial choice to make him not guilty of Precursor actions, but it’s not by any means the only interpretation that I think works, or even the only interpretations that I want to explore in my own fic!

Basically, I’d say it’s entirely up to the fic author, and I count the novelization as a fic as well. It’s a film. We literally don’t have canon on what’s going on inside Newt’s head or how he feels about it at any given moment except when he cries over “They’re in my head” while they try to make him kill Hermann, the one thing that was so clearly against his own desires that he actually gained the power to break free long enough to speak clearly. Everything else? Maybe Charlie Day knows or has a set belief in which scene was which in terms of how much of the Precursors it was, but unless he spills on a frame by frame level, we as the fans have no idea what blend of Newt/Precursors we’re seeing except that one time, in my opinion. It’s entirely up to interpretation and what tells a better story!