I have the exact same problem. As soon as I animate the position of an attachment point in sequencer, the cable resets on every frame until the attachment point comes to a stop, then the cable relaxes again. Exactly like your example video.
Did you find a way to fix this? I really hope you did and don’t mind sharing! This cable actor does exactly what I want but I just can’t get it to work in sequencer when attaching two moving objects. Argh!