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

Records of the Grand Historian, Yin Benji, and Book of Documents, Tai Jia, record that after Tai Jia ascended the throne, he was tyrannical, so Yi Yin exiled him to Tonggong; after three years of moral cultivation, he was restored. The novel's mention of the Shang king lineage aligns with official history.