I’ve had a look back at in-the-sky.org (although visually clunkier than Stellarium I find it easier to use). Two things that I think I’ve worked out.
1) The screenshots below seem to be a match, (YouTube Time Code 0m25s and 00h54m16s PDT) and the animated passes of Satellites that follow seem to match in the video too in their relative positions in the sky. So that might be a place to start from for others when trying to make a true synchronised video.
2) If this time sync is correct ... Read even more