so just as reminder, yes, Jinx was at the Brotherhood of Evil meeting along with almost every villain thats introduced in the show. shown at the end of episode "Homecoming part II" (54th overall episode)
continuity conflict aside, its safe to assume Madame Rouge followed up on her words of being in touch with Jinx (and subsequently, the rest of the HIVE FIVE) and got them on board with the Brotherhood of Evil.
also safe to assume that episode "Lightspeed" happens before "Homecoming part II"
(TT03's Fearsome Five fanservice before their companion comic "debut" lol)
now i personally have my own scenario around this detail alone, headcanon territory here,
Jinx and the rest of HIVE FIVE (six) eventually got the invitation, however it didn't happen overnight (just look at the huge villain roster. some were goners— did they ressurect them? well, it must've taken them days or weeks regardless),
so theres a hypothetical time gap in-between where Jinx would rethink of her life decisions up to that point and have some dilemma around her alignment. would she want to put up with peers who barely respect her as a person like Madame Rouge? perhaps Kid Flash still patrolling Jump City while the Titans's are still off town and thus more banter and development between Jinx and him.
and eventually lead to her having made up her mind and Jinx decided to not want to do the Brotherhood's dirty work anymore. however, to not rise suspicion (since Madame Rouge saw her setting Kid Flash free), she attended to get information and serve as intel.
she'd leak the info and what entailed in the meeting to Kid Flash later, a whole scene of trust, lead to her breaking his communicator so they wouldn't be tracked, and they run off to the night.
they probably did stuff behind the scene, maybe letting other Honorary Titans know or taking care of enemies that aren't on screen or something, and thats why they came in late.
i'd imagine for her to be in the Titans Together episode's big fight and fighting alongside the Titans, and Kid Flash referring to her as a "friend" (or girlfriend, if you watch in JP dub), there must've been big development off-screen for that to happen.
and yes, at the end of the day, season 5 was objectively rushed and they probably lack hindsight or didn't think much of the continuity errors when they worked on it.
but the best thing about fandom is to fill the gaps in-between, and personally instead of dismissing those errors just for things to make sense for oneself, like lots of dudebro theorists on reddit, i tend to go with the more whimsical "how can we make this work?" mindset.
that way, more scenarios can be made, and animation/continuity errors have purpose haha. I keep my eyes peeled when I watch or rewatch shows or movies or cutscenes because of it, to notice every single detail. maybe i can make new ideas or headcanons!