This is one of those effects, you can probably achieve in multiple ways. One method would be to create each line of text and add two linear transition effects. The benefit of this is that you can move your text, all over the screen, but the linear transition, stays in the same place. If you use masks, the masks will move with the text. So with a couple of linear transitions, you can basically create a track matte, without having to need a different matte for each layer.
In the example video, there was some overshoot on the text, so in my example project I created the same overshoot. But when the text exited up, it was masked at a lower point than it did with the overshoot, so to do that, I keyframed the top linear transition effect.
Check out my example project, and if you have any questions ask, or perhaps someone else might have a better method for this. 7385_lineartransitionfolder.zip
Johnny Cuevas, Editor
"I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work."
---THOMAS EDISON on inventing the light bulb.