This scene in Pretend Like It’s The First Time (the alternate universe episode) had Jayce walking through a bunch of Viktor’s Soldiers/Hextech dolls, we can see one that looks a lot like Caitlyn if she was a Hextech doll.

Same bloody eye, and (this part’s not in the image) same shoulder guard thing I think that’s Caitlyn. But am I tripping ?

I did some math, using Caitlyn's height compared to the distance between herself and Jinx as well as the time it took for Jinx to close the gap, and came to the conclusion that Jinx moves at around 30 ft/s.

I think that it was Silco's soul or ghost or whatever you want to call it who was able to temporarily force his way back into the living world to give Jinx advice.