Gen. Wallace was in West Tennessee for a brief time in June 1862. Maj. Gen. John A. McClernand of the First Division, Army of the Tennessee commanded forces which entered Jackson, Tenn., June 7, 1862. Wallace commanded the Third Division, which occupied Bolivar.
McClernand had borrowed one of Wallace's regiments, the 78th Ohio, Col. M. D. Leggett. It happened to be among the first units to march into Jackson, and may the cause of the confusion. Wallace was recalled shortly afterwards due to questions arising from his part in the Battle of Shiloh. Rarely afterwards did he have another field command.
For the remainder of the war, Jackson was occupied by troops of different units under different officers. It did not have a permanent garrison or post commander. In order to know who was in command, we would have to know the year and day, or at least year and month.