Okay, so it looks to me like there's no bug here. Instead, what you're overlooking is that NeoLemmix has a replay mode (much like Win95 Lemmings; Cheapo; Lemmings 3D; etc do). So, when you fail a level then immediately replay it (or quick-restart with the restart hotkey), it repeats your previous actions, until you interrupt it, which you can do by taking an action (such as assigning a skill, or changing the release rate - but note that simply selecting a skill won't interrupt it), or by clicking in empty space, or by pressing the "cancel replay" hotkey.
NeoLemmix being in replay mode, is indicated by the red R on the skill panel. (If the R is instead blue, you're also in replay insert mode - this means that any new actions won't cancel the replay, they'll just be added to it. Assuming you haven't reconfigured it, the hotkey to go in and out of replay insert mode is either W, if you're using the traditional hotkey layout, or O, if you're using the functional layout.
If you believe you are also having issues that are not explained by this, let me know - however the particular video you've posted is in replay mode. I'll leave this topic open until I get confirmation (or a counterexample) from you.
(In case it's of interest to you, I'll also note that NL goes far beyond just having replay mode like those others do - you can also rewind time; open a menu to delete only specific actions from the replay; save and load these replays to/from files... let me know if you want more info on any of that.)