Ah...another one of these types! This time they call the FMC a villainess instead of Ice Princess...oh boy!
Her reaction when he walked up to her the first time makes me think she knows more about him AND has an interest in him than she lets on. She just probably likes to play the villainess role and that extends to her interaction with him when they walked behind the school. She has to keep up appearances to everyone else after all and with that I bet she will be SOMEWHAT nicer to him in private at their new home.