Stapfam - from which end did you begin winding the tape? The top of the bar or the bar end?
When I were a lad, growing up in the old country, we always started at the top with a couple of overlaps and ended at the bar end. However, when I got back into biking here in the US some years ago, I found they did it the opposite way( I also noticed they drive on the wrong side of the road
) with the need for sticky electrical tape in the center of the bars to hold down the tape ends. This tape eventually becomes unstuck and is a nuisance, not to mention ugly. I stay with the old way and have never had the tape unwind. The most difficult bit for me is making a neat tuck into the bar end and inserting the plug.