"But what did she [Rachel] want?"
Girl, Rachel literally got herself burned on a stake for you, then reincarnated as a dog to be with you. What do you think she wants?
Either way, it seems like the dog is going to get.
Also wonder if umbrella chick is also someone from their past? Maybe another party member? Maybe not all she noticed was Rachel's ears and tail she didn't seem to recognize Rachel herself.
My impression is that she is from some kind of secret magical society who monitor transmigrated folks, and probably keep their existence out of the public's eye. Xiya is very good at blending in, so she probably had little contact with them, although they may been monitoring her already. And Rachel just stands out like a sore thumb.