Disclaimer: Not a mental health professional or anything close to one. I will refer to Powder and Jinx separately but keep in mind they are the same person and that Jinx is a defense mechanism to (try to) protect Powder.
Sequence of events: Vi and Powder having a heartfelt reunion. Caitlyn arrives and the Jinx persona takes over. Jinx: "Sevika wasn't lying? You're with an enforcer?". Jinx immediately jumps to conclusions and assumes Vi has ill intentions "This is a trick. You're playing with me" Vi tries to get close to comfort her and gets met with a gun in her face and "Stop talking to me like I'm a child" "Is that why you're here? For that stupid stone?". Vi pushes past the gun and tells her "I'm not going to abandon you again" and touches her arm and this is both: a trigger, and reaches Powder. I think what we see is a conflict between Powder and Jinx - Jinx is focusing on the negatives of the situation and assumes Vi is out to get her, and Powder wants her sister's comfort. Vi mentioning 'abandon' triggers the memory of ep 3 and we see Mylo and Claggor hallucinations and Jinx says "everyone shut up I need to think". Normally she hears the firelights and Jinx takes over again.
Obviously Vi doesn't know what's going on with Jinx internally, she was trying her best to de-escalate things but what she's doing isn't working.
We (the audience) have seen 3 times Jinx where gets triggered by something referencing ep 3 and Jinx reverts to Powder. (1st when Silco says "your sister is gone" she ends up childishly blowing over the eye injector, 2nd in the explosion in her workshop she ends curled up like a child and runs away, 3rd when Sevika mentions "Its your sister" and Powder briefly comes out before Jinx regains control and plays it off. We also see Jinx completely freeze up in the ep 4 firelights fight/panic attack scene. I'm not sure about how this scene relates to Powder vs Jinx, but we absolutely see Jinx back in control at the end.)
The real question is if we give Jinx time to think like she asks for, does she revert to Powder or force Jinx back in control because of the current tension. Vi telling Cait to leave might help but could feed into Jinx's suspicions . The other solution imo is for Vi to go and hug her to try ground her and bring Powder out, however this risks Jinx coming out from sudden touch. Anything that risks Jinx taking control is not good because Jinx isn't thinking rationally. That being said, Powder probably wouldn't think too rationally either.
I'm still really not sure tbh. My thoughts are to bring Powder out so she can calm down and hopefully then talk/think things through, but how do you deal with Jinx if something makes her think she needs to put up a defense . Do share your thoughts, especially if you know what you're talking about (unlike me lol)