I think Tiller and Hart were supernumerary officers at this point. We don't have a record of Hart's battery again until September 1864, so my theory is that all of the enlisted me from Hart's second organization were left with the Army of the Tennessee, probably consolidated with either the 19th or 24th Arkansas, thus making Hart and his officers Supernumeraries.

Were supernumeraries paid, or paid at the same rate as officers assigned to active units? If not that could explain why Tiller was seeking an appointment as a Cadet rather than revert back to the ranks.