Create a new text effect project.
Pull the text layer into it's own group. Call the group, Text Move.
Rename the text layer, Text Mask. Trim it to the length of your transition.
Clone the text layer. Rename the clone, Text Color.
Create a new group above all the other groups. Call it, BKG.
Inside BKG, create a black solid. Trim it to the same length as your text layer.
Add an image mask to the color solid and invert the mask in the inspector. Drag the Text Mask layer onto it.
Add a Move behavior to the Text Move group. Trim to the length of your transition and adjust until the text is completely covering the frame. If the text looks rasterized, change the render quality to Best.
Add a fade in/out behavior to the Text Color clone layer and adjust so the color fades away (leaving only the mask) before the transition has completed.
To get this to work with different lines of text and to be flexible, requires knowing how to rig and is much more difficult. Basically, you need to create a text effect where the transition is at the end of the effect protected by a build out mandatory marker. You need to create adjustable parameters for the Move behavior at the least.