I'll have to go back to re-read and confirm - but I think there was some lore about how, at least in a 'folklore' sense, some of the cats of that town were highly spiritually-linked.
So if the white cat's the same (and, c'mon - it's possessing Maki, you can't tell me this ain't spirit-y stuff), I suspect the line will be that this cat is connected to them both in some fashion from when they were kids, and is doing this to heal the rift between them by making them both be honest about what they truly want from the other.
But they're on a timer because the cat will also just fully erase Maki unless they can "break the curse" or whatever (kissing / gex / whathaveyou).
So I guess we'll see. Though I wonder if the next chapter has NekoMaki actually giving insight to Ichika on any of this, or if it'll be more half-answers (if anything), or if it'll be more nekoyuri time (or some combo of all three, of course).
Thanks for the TL as always.