Inhibitor I / II prevents automaton from weapon skilling in alliance setting.

[ikudosi]

When in an alliance setting and using inhibitors (but not speedloader), the automaton does not use it's skill.

[Tsukihika]

If Puppetmaster has enough TP, automaton with Inhibitor attachment equipped will always wait for master to WS first, in order to trigger skillchain from player weapon skill. This is completely normal Inhibitor I/II specific behavior and has always been like this. One does not even need full amount of TP to trigger this wait-for-master-WS behavior. It triggers somewhere around 800 TP or something closeish to 1K. Also Puppetmaster is the only person in party their own automaton AI will react to. It does not wait for other party members to WS first ever. Only the TP of their master matters in regards to Inhibitor attachments. If their master does not have sufficient TP, then automaton will use their TP/WS as soon as possible, regardless of the situation. And will thus skillchain with party/alliance members again and use whichever weapon skill they have at their disposal, that closes the skillchain.

Also quick random pro-tip: you can remove and equip again your own weapon to reset TP and automaton will once again use their TP/WS whenever possible, provided master TP stays below the wait-for-master-WS trigger condition. This way you don't have to engage the monster and risk getting hit by dangerous AoE abilities / spells. Or can simply run in and WS it away if prefer. :3

[ikudosi]

I will try again on next Divergence but I am positive I tried that. I was ultimately forced to remove inhibitors.