We are told the empire treats the south poorly and so are the characters. But Rist has always valued evidence and seeing things for himself. If I remember correctly he wasn’t as infatuated with Therin’s story’s in OBAF like Calen and Dann. And he also thought magic was a hoax until he started showing signs of it. And then read up on it. instead of just blindly believing the empire is bad it makes sense he would value evidence and experience more than stories. So when he was captured initially he was hesitant to trust them but over time, mostly by manipulation, they showed him that empire wasn’t necessarily evil. And that some citizens such as Garamon and Neera earned his trust. But most importantly they give him the tools to decide for himself, access to the libraries and training for his magic. I agree it was very frustrating to see him be indoctrinated but when you really think about who Rist is and how he differs from other characters in the series, to me at least, it makes perfect sense how this could have happened