She's entirely on the up-and-up. She has mysteries to her, sure, but they're pretty obvious if you pay attention to certain details (for reference, the title page artworks for each chapter showing Tsukasa in different places (and possibly times) are actually legitimately canon clues and so is the reference to the Tale of the Bamboo Cutter).
She does, legitimately, have affection for him, she's just a lot more in control of herself than he is. This is still all very new to her, though; despite her thousand-plus years of living on this planet, this is the first time she has ever experienced proper mutual love- she is the happiest she has ever been since she was 'gifted' her immortality.
For reference, I don't really know specifics, but I am aware of certain details thanks to having seen both seasons of the anime and the four-part miniseries about Nasa as a high school teacher. Both the intros and later episodes give some serious clues as to her mysterious nature.