Oh, true.
...I hate weird plot stuff
Yeah, I think that Jack Noir went back in time after Becquerel was prototyped. Mainly because the trolls session was long over when the kids session started, but Jack Noir still arrived there
after Becquerel was prototyped, which was in the kids session. However, it is unknown
when in the Kids session he traveled in time, because his arm was bloody, which would mean he was in battle, but it would have to be after he killed Bro, because he had Lil Cal, but his arm wasn't bloody after he killed bro, which would mean that he actually traveled back in time far later then the story has progressed thus far.