I have no problem with how the Phoenix origin meshes with the previous films. It was hinted at, all through out X1, that Jean had some issues with her powers. Particularly concerning the use of Cerebro.
Remember at one point she's explaining why she can't use Cerebro and she says (and I paraphrase) "For someone like me, it could be...." "Dangerous" Cyclops says finishing her sentence. Then the look on her face is fascinating. She looks as if she's ashamed or trying to give a short explanation concerning a topic she doesn't want to discuss.
THEN, Cyclops is frantic when he sees her entering Cerebro. Why? Does he know that Jean is unstable mentally? Does she even know it? Or has the professor just fed them a story about it being physically dangerous just to scare them into walking the line?
To me it's obvious that Prof. X has some concern that Cerebro's amplification abilities will undermine his "work" he's been doing with Jean.
Cerebro may or may not have contributed to the release of Phoenix, but it advanced the idea of Jean being unstable before the Liberty Island incident. Her expression after exposure to Mag's machine is clearly designed to insinuate that something has happened. We don't know what that is....it could have amplified or evolved her powers but with all the talk about Cerebro before, it seems to me that the radiation released powers, not amplified or created them.
So in X2 we see those powers starting to manifest. In the Cyclops attack sequence, Jean looks pretty mean at one point. She also seems to struggle with controlling the power.... whether with the fine control (tweaking the missile fins) or with big outbursts (when she damaged the dam). We could assume that it's her learning how to use her powers ....
....or we can think that possibly the struggle she's having is with restraining the intense emotions she's having while using them. Seductive emotions.
Her "death" basically evaporated any mental blocks she had left and also any self control too. So when she comes back in X3 the Jean we know is now the repressed persona. A reversal of minds.
Then X3. I do hate that they ignored the X2 continuity and forgot the flame effect. BUT if I'm not mistaken, for an instant before she gets vieney, there is a flash of light in her eyes. Maybe I was seeing things.
Anyway, the scene where Prof X explains Jean's issues is WAY too rushed. That could have been a much nicer scene if it had been stretched out abit. I did love that it cast X in a light that is a step away from the perfect goody-goody from the previous films. Anyone who's read the comic knows he isn't perfectly nice all the time.
The explanation of the title "Phoenix" could have been handled better. Either as another descriptive line by Mags ala him calling her a goddess or as her codename that she never felt comfortable using because she never felt strong enough to be on the team....but events of X1 forced her into the field. blah blah.
Jean and the Prof almost remind me of those kids I knew who had very strict parents.... once they got out from under their thumbs, the kids went wild. Phoenix is like a drunk, drugged out, resentful teen. She may love her parents/Prof X but in her rageful stupor she says and does alot of things she'll regret.
In my perfect world I'd like to have seen Cyclops been found unconcious with Jean.
Basically a similar infirmary scene but instead of asking "Where's Scott?" he'd be shocked at Jean being hyper sexually aggressive while Scott lay next to her unconscious. That snaps Jean back in where she asks Logan to kill her (cuz she knows what's happening inside her).
Scott could remain out until the Prof death scene which mentally shocks him awake. The Prof could in the last moments telepathically let Scott in on the details of Jean's true condition.
Scott then leads the team to the last stand. Here after everybody heads for the hills, Scott and Logan stay. Scott telling Jean he loves her is able to approach her without getting killed because Jean is struggling against Dark Phoenix to protect him.
Lot's of personality flip-flops here. Jean begging Scott to leave because she can't protect him much longer. Scott refusing. Saying he'll die first. Jean says "No, I will".
With that she telekenetically launched Wolverine, claws first, into her. She dies expressing her love for Scott.
Logan is devastated at killing her even tho she really committed suicide (like in the comic).
Later at the mansion, a nice scene where Scott tells Logan it's not his fault.
AND,
Angel never leaves San Fran until after the last stand (that'd clear up that cross-country Mach 8 flight of his)
Iceman, while evacuating, would create an ice path across the bay for everyone OR as Mag's powers fail...(the bridge should have fallen ..the supports were destroyed) and Bobby could have iced up some supports.
-Dallas
I think the movie explanation made it very straightforward and I can't wait to rewatch X1 and X2 again knowing about the "explanation"!! 
