Alex transferred his year-long ownership of the courtyard to Jai Heiyun that very evening. Then he spent the entire night chatting with her about various things while helping her with a lot of different things regarding the tournament.
Because Jai Heiyun was newer to the Medicine World, she wasn't completely aware of where everything was. She knew about the broader aspects of the world but because most of the minor information was kept in talismans that she took out to check from time to time, she could no longer figure out what she had to do once her access to her Soul Space was taken away.
Alex taught her about everything he knew in as much detail as he could to help her. Considering Jai Heiyun's cultivation base, he didn't see her winning the competition or even coming close to it. She lacked both the knowledge and the strength for it.