I think that is a perfectly valid reason to because logically now you have to question does she like you at all? only because of time travel? is she even on our side? Skylar has always been towards the lower half of girls for me and if she didnt have such prominence in the sex stuff early on I would remember her as much as i remember the brown hair henchman (whose name i forget ), and even with little care the whole reveal was still pretty sour for me I cant imagine how immeasurable your disappointment was or how much your day was ruined.Do you live in my head?!? Really nicely explained. It feels like our MC is deceived (Legit. This is an original, and story) and for me personally ruined the intimacy of a scene I had been really looking forward to.
I wonder how much of this would be "fixed" if she was clearly "off" when giving the explanation/during the date because as it currently stands she is objectively hiding the truth from MC for her own benefit (she gets food and dick if she lies if she tells the truth she might not even if shes doing it under "orders" , or future mc told her to, or whatever
She doesn't need to feel "off" because what she is doing is the right thing not because of any in universe logic or moral reasoning, instead she is in the right because she is a LI in well written VN and therefore cant be a villain