Creating resposive background for text layer for lower third title

I would animate the text layer's position and add a tracking animator. This could be saved as an animation preset. 

I would then add a shape layer with some expressions to control the size and position of the rectangle so that it lines up with the text. The position of the shape layer would be tied to the Y position of the text layer with an expression that allows you to animate the X position. This could also be saved as an animation preset.

I would then add Set Matte to the text layer and select the Shape layer as the Alpha Source to wipe on the text. 

Here are the expressions I would use for the shape layer:

// Rectangle 1/Rectangle 1 Path1/Size:
src=thisComp.layer(index - 1);
ref = sRc.sourceRectAtTime(2);
refScale = sRc.scale * .01;
x = ref.width + 300; // add 300 px padding
y = ref.height + 50; // add 50 px padding

[x * refScale[0], y * refScale[1]]

//Rectangle 1/Rectangle 1 Path 1/Position/
src=thisComp.layer(index - 1);
box = src.sourceRectAtTime(2);
refScale = src.scale * .01;
x = box.width / 2;
y = box.height / 2;
t = box.top;
l = box.left;

[value[0] + (x + l) * refScale[0] + 150, (y + t) * refScale[1]]

// Shape layer Position
ref = thisComp.layer(index - 1);
[value[0], ref.position[1]];

This is what the comp looks like:

It's not a perfect match, but it is close.