where this was the 3rd time they interacted, the first was outside of school, and she was kind to him each time, as opposed to the rest of non-Emma nobels who act extremely stuck up to him. He gets takes with her beauty, grace and lack of jerkishness. He is so fed up with being treated like dirt that he will go to extreme lengths for those who do not treat him so.
She wanted to talk to him because she wanted to ask him if he had Olivia's skill modifying abilities (there was a 2nd stage to the entrance exam and he "threw" it by making a deliberately small stone bullet, but Olivia was the only other person in history who could make one that small and she was aware of that limitation on the size ranges of the spell) as she knew olivia's abilities were her best chance of not dying.
Though why her family never tracked him down in the first place since Great Sage is pretty much the best hope of finding a way to cure her is beyond me. but their society seems to be run by idiots who do not bother checking for skills on the level of value they could be used to save or destroy nations (seriously he could discover every dirty secret they have and give any enemy nation a massive espionage and military boost if he got fed up and left the country).