Is “Yi Yin exiled Tai Jia and restored him after moral reform” true?

The Records of the Grand Historian, Yin Benji, and the Book of Documents, Tai Jia, record that after Tai Jia ascended the throne, he was tyrannical and was exiled by Yi Yin to Tong Palace, where he cultivated virtue for three years before being restored. The novel mentions that the lineage of previous Shang kings matches official historical records. According to the Records of the Grand Historian, Yin Benji, the original text states: 「帝太甲既立三年，不明，暴虐，不遵汤法，乱德，于是伊尹放之于桐宫。三年，伊尹摄行政当国」