Interesting, I indeed tested it with a wired controller! I guess I'll bother Wyz, the author of the plugin, about it. Let me know if using XP makes a difference.
About the bug, I definitely did this on purpose, thinking it feels natural. If I understand you right, you would prefer it if you walk off a platform, start falling naturally, then only be able to jump once? I initially had it like that and didn't like how limited and restricting it felt, especially when you meant to jump off a platform and walked off instead by 1px, then suddenly 'couldn't' double jump - that actually felt more like a bug to me! Hope that makes sense.
Thanks and good attempt at the last level haha!