I helped a friend do this some time ago. It took us several attempts to complete it and we came to the conclusion the timer starts as you approach the ledge, even before you drop.
For each of our failed attempts we paused a bit before the drop (to figure out who goes where, for some reason we changed the plan every time lol).
On the successful run we did not pause.
So, did you pause?
Not saying it’s not bugged, just sharing my experience in case it’s helpful.