It looks to me like the cut was OK and the sail did fly in front of the boat. The sheet was wrapped around the winch but it is not clear that was the problem. It might have been but I would give that a less than 10% chance of being the problem.
The problem was that the sail was not pulled in fast enough. In the words of Don, the sail need to be pulled in as fast as possible and that clearly was not happening.
What I cannot tell is if the new sheet was stuck, perhaps under the jib, making it impossible to bring it in or if it was just not pulled in fast, perhaps waiting for the boat to jibe first.
The lazy sheet should be set on the webbing sheet holder and dressed inside the lifeline with the sheet taught before the jibe. We should make sure it is above the jib so it will not hang up. The lazy sheet should slightly creas the luff of the sail. Then when the jibe happens, it is pulled in fast. Ideally the spinnaker would fly in the new side before the main comes across. We have never had that happen, but that is the goal.
