Okay, my plugin is one of the ones involved here. Let me take a crack at this.
The first thing I should point out is that I use Yanfly's Skill Learn System plugin in my main project, and of course the Dualtech plugin as well (my plugins are made for my own purposes first) and have no problem. I haven't updated my Yanfly plugins in a while, but I have no idea why that would make a difference in this case. EDIT: Updated Skill Learn System to Yanfly's latest; no repro as of yet.
A little more information would help:
1. Which plugin is listed first in your Plugins window: Skill Learn System or Dualtechs? (For me, Skill Learn is first.)
2. Is the Dualtech listed as a skill you can learn from the Skill Learn system? (For me, the answer is no.) EDIT: Made "Fire Power" dualtech a learnable skill instead of one automatically added. No repro. Whether Carol (the second party member, and not the one learning the skill) was present in the party had no bearing; skill was learnable and even displayed correctly, though due to the nature of the Dualtech plugin, skill was of course not available when Carol was not in the party after being learned.)
EDIT: Just noticed you had skill learn system integration turned off. Haven't tried that. Lemme see what happens. FURTHER EDIT: Nope. And apparently the integration doesn't do what I thought it did anyway.
FINAL EDIT FOR NOW: Sorry, I'm so far unable to reproduce this issue at all. There's more I could try, but it's late and I'm sleepy; I'll hammer on it later.
One last thought for the night is that maybe a space snuck into your Dual tag? I forget how Javascript handles that, but probably not well. But it's not listed when you wrote what you had in the tag, and you said you see the issue event when you remove the tag, so that's probably not it; just a guess. If you can zip up a copy of a project that has the bug (just make a new project, make the bug happen, and remove all data files) I can look at it when I have the time.