The situation closely resembled what is commonly known as dissociative identity disorder, also referred to as double or multiple personalities.
However, Xiao Yi's case was slightly different. He never displayed behaviors typical of multiple personalities, even if he occasionally pulled off astonishing maneuvers. These acts weren't vastly different from his usual self, simply making people wonder if he was truly a genius, rather than asking, "Who are you?"
Moreover, there were no interruptions in his memory, among other things, which didn't quite fit the profile of multiple personalities.
Therefore, Xu Yingguang tended to believe that what Xiao Yi referred to as his "other self" was not another personality. After all, distinct personalities would be considered separate individuals, not another version of oneself.
What he meant by "another self" was probably closer to the ego, the id, or the superego.
Thinking about it this way, it seemed to fit.