It may be some time ago since I read the novel, but wasn't his first encounter with her supposed to be after the fight with the demon? Don't really remember.
You remember right but that happen in the web novel, after he beat the demon using a disguise, she arrive and ask to him if he was the one that defeated it but he reply "it was a masked hero, if you don't belive me ask to someone", this reply come from the fact that he used an illusion for make appear that after the hero defeated the demon it just went away... obviously she returned attacking Satou but he simple avoid being hit... personally I don't remember if she simple continued to attack making him interesting in the eyes of her parentd or after that a training duel was made resulting in her parents lay their eyes on him.
If I remember right she was interested in hayato but after he went back home she changes the target to him... btw I'm not really sure about this.