I think he is a descendant of O'rin and Sakuza. O'rin was likely a mistress of the lord a long time ago, but something terrible probably happened (likely Sakuza either died, Sakuza's legitimate wife didn't want him seeing O'rin anymore, or O'rin died) and they could never be together again. Whatever did happen, O'rin probably gave birth to an illegitimate son beforehand. An unknown amount of years pass and that illegitimate son started a family and generations down the line comes Jinzaemon. The tragic/horrible circumstances of O'rin's death made her into a dangerous Yurei spirit, so she continues to haunt the land, forever calling to Sakuza and the son she never knew. Jinzaemon's father probably had some idea of the situation, likely through an old legend passed down and by hearing O'rin's melody himself but somehow being able to resist the call, and that's where we get the warning Jinzaemon mentioned. Something must have changed, either Jinzaemon was especially weak-willed or O'rin became more powerful and now the melody became irresistible. In the end O'rin happily departed for the afterlife, taking the soul of her "son" with her. Jinzaemon died because of the sins of his ancestors, but at least O'rin's curse is broken and she will no longer haunt the land and murder anyone she encounters.