In Tokyo Ghoul: Jail, Rio's personality before the 'Jail' incident of being imprisoned if unknown, as hes has seemingly changed greatly from both his time in Cochlea and Anteiku, casting aside any of his own personal needs, now only focusing on working to find out who 'Jail' is and why he was imprisoned instead of Jail.
A part of Rio's personality that remains is that he cares deeply for his unrevealed 'Big Brother' who is thought to be imprisoned in Cochlea by Rio himself. The reason Rio took liking to Kaneki so quickly is that Rio stated that their personalities 'overlap'