I definitely disagree. What was the tone of TG? (And it's OK if you can't put your finger on it, because it may not have a consistent one).
I think younger generations (or those who just haven't seen it in a while) forget that "The Terminator" was a horror film (with moments of body horror w/Arnold in the hotel room). That was the tone. The T800 was the sci-fi equivalent of Michael Myers or Jason Vorhees: a relentless shark that just kept coming. That's f'n scary if played right. Hell, anyone who's had a nightmare about being chased by something that just won't stop understands how terrifying that can be on a visceral level. That's the movie, and it's consistent throughout.
T2 had a different tone. It was bigger, more polished/action-oriented, and was saying something else entirely (if the T800 is an analog fear - a tank that won't stop hunting, though at least you know what you're running from), the T1000 was really analogous to our digital/tech/internet fears (an enemy that can be anywhere/anyone). Different theme, but consistent in what it was. Any humor came about organically.
By the time you get to T3 you're throwing stuff at the wall. It was clear when Arnie put on their sparkle-glasses in the convenience store (a very "wink-wink, nudge nudge, hey it's just a movie, guy!" sort of thing) that the film didn't know what it was. "Generic action film with sci-fi elements" and "sporadically self-mocking" aren't entirely consistent and don't give your film an identity that an audience can identify with.
T4 was... yeah.
This seems from all the critiques like it's going in the T3 direction of trying to be all things - an action film, a love story, self-mocking/referential" without really committing to any of those things (or whatever else it borrows from). So yeah, tone matters quite a bit. You know when it's off instinctively, even if you can't articulate it.