Relative timelines animate from whatever the current value is to whatever the final keyframe is. So if you want to reset rectangles to their original position you need to add keyframes for their final values.
You need to animate every property that changes on every rectangle on every timeline into its final size and position. Currently you are just animating one rectangle to its final position. I filled in timeline '1' in your document:
relativeTimelines.hype.zip (18.1 KB)
Also here is the example from the video:
WooGrit.hype.zip (1.0 MB)