The video overlay has its own origin, which is independent of the drawing origin. The video origin only has an effect when the output is mirrored. In mirror mode, only a quarter of the video frame is used. The video origin allows you to continuously change which portion of the video is used as the mirror source. By default the video origin is (0, 0), i.e. the upper-left quadrant of the video.
To change the video origin manually, move the mouse while holding down the Shift key. The video origin can also be automated, so that it makes random jumps in sync with the tempo; to enable or disable random jumps, use Image/Video/Random Origin, or Ctrl+Shift+R. Note that in either case, video origin motion is affected by Damping.