In retrospect I should have read Carnelian's perspective again, she specifically mentions that Rin
didn't end up with Nerine. That wouldn't necessarily be inconsistent with this being the main timeline Rin is in in the other snippets, but would be relevant to consider for the status of this snippet. So now we have something like...
Timeline 1: Primula original, Rin x Nerine, Tick Tack! time travel leads to...
Timeline 2: Rin attempts to save Lycoris further back in time, unknown other effects
Timeline 3: Carnelian's timeline, Rin x Sia
Timeline 4: "main story", Like Timeline 1, except earlier, and Primula is observing and Carnelian has come into it
And Timeline 2 there might also be 3, but it's definitely not sure if that's the case or not. Heck, 2 could be 4, if Lycoris' death is faked to avoid paradox. We can assume it's not both though, since the main story is explicitly not Carnelian's timeline, according to Word of Primula.