i'd start by creating the track matte in a new comp. create a bunch of rectangles that fill the screen, go to about 1-2 seconds down the timeline and add position keyframes for all the rectangle layers. then move back to the beginning of the comp and slide them horizontally off the screen. then just tweak the first and last keyframes of thow layers to make them move on screen randomly.
bring that matte comp into a new comp and bring in the footage layer bellow the matte layer, then, for the footage layer, select 'alpha matte' from the trkmat menu in the 'modes' panel on the timeline.
if you scrub the timeline, you should see that footage layer reveal.
the footage layer is independent from the track matte, so you can animate the postion, change the scale add color effects, etc, without effecting the matte.
so now you can just duplicate both the footage layer and the matte layer, adjust the timing of the reveal by moving the matte in the time line and triming the footage layers to match the new in-points, then add position changes, scale and/or effects to the footage layer (from the looks of it, they used tint or tritone for the colorizing).
do that five or six times and i think you'll be close with various changes to the footage layers.
if needed, you can make different track mattes for some of the footage layers to change it up a little more.