I think if she really did spawn from Kairi, it was on the night of the storm. It's the only occasion we know of that makes sense. Alternatively, an event we don't know of.
I do tend to believe Sora's Memories are affecting her though. With how much the game's supposed to be focusing around the Organization and with how little they were shown in the trailers, and the whole trailer focusing around Xion, it's hard for me to believe they'd just 'accidentally' show parts about Sora's Memories without them being Xion-related.
KH2 showed wonderfully Sora didn't know what Kairi looked like in KH2 in the scene he imagined dancing with her in Halloween Town. Thus, if Xion was affected by his Memories of Kairi/Namine (which were messed with the most, not just added/removed during CoM) she would look like KH1 Kairi.