I'm flattered, Ariel, but with all due respect, I think the "movement" began a long time ago. I don't think "introspective music" is a new genre, and I definitely don't think either of us invented it.
If you'd define what you mean by it, I can probably give you lots of examples from before your time or mine. If you want music that combines no-nonsense honesty with thoughtful observation of self...
Elizabeth Elmore, The Reputation, "This Town"
There must be something wrong with me
'Cause everyone else makes it look so damn easy
I spend all my nights removed and watching carefully
And all of those guys who tear me down
They seem so nice when I see them around
But maybe they're right and just letting me know
I don't belong in this town
David Nields and Nerissa Nields, The Nields, "Snowman"
I don't feel much like dancing
You scrape the ice off my glances
We walk through a cold and moonless winter night
You recognize the coal in a snowman's eyes
It's all right, it's okay, if I freeze I can't decay
You touch and I freeze, there is ice where my heart should be
I'm a snowman
Cold is all I understand
I'm a snowman,
You can't hurt me, no one can
And those are just what I'm coming up with off the top of my head. And, of course, the lyrics typed on the page don't even come close to conveying what they do in the context of the song.
And not only that, but I think that sometimes the most effective songs combine introspection with observations of the rest of the world. If your song only talks about yourself, then I don't have any way of knowing if you're telling the truth. But if your song spot-on nails what Christmas is like in your family, or what goes through everyone's head at meetings when that one woman gets up to talk, or why nobody wants to be the first person to arrive when that one guy throws a party, and if I agree with your observations, then I'll think, "Yes, that's absolutely right, that's exactly how it is," and I'll listen more carefully to whatever else you have to say, including your observations about yourself.
It gets complicated, because you can argue that everything just takes place in our heads and that there is no absolute truth to be observed. But I don't really want to get all philosophical; I just want to say that changing the point of view now and then can make the song better.
It's not necessarily an either-or thing. In "The Song Nobody Knows", the line "Looking out the rain-streaked windows as the bus goes by" is about the narrator -- me -- but it's not about what's going on inside my head. Maybe it's what the guy sitting across the aisle saw. The next part, "Do you share my sentiment?/Do you feel the way I feel?/Do you know the song I know?/Do you know how it goes?", goes right back into the introspection that characterizes the song, but I feel the song is more effective because I'm not being introspective the whole damn time. Same goes for "When I was six years old, I wanted to change my name/Now I just want everyone to know who I am". I feel that's one of the most effective moments in the song because not only am I crossing the internal/external boundary, I'm pairing it with a "then/now" change and a cadence in the music.
Was I thinking about all that when I wrote it? Hell, no. I just knew that I liked it a lot. I'm not saying that, as a songwriter, you have to map out these things before you begin writing. I usually discover them later. I don't think it hurts to be aware, though.