Mary --
The entry "commanding the company" simply means this was the officer senior officer present for duty. Evidently the captain was not present. There are no paroles for Confederates at Washington GA. Each member of President Davis' escort was given a Spanish silver dollar and went home from there. Their commands were never formally paroled.
As for the 13th Tennessee Cavalry, elements of this regiment remained in central Tennessee after Wheeler's disasterous raid of August-Sept. 1864. About three hundred members of this brigade came out of Tennessee with Forrest in late September, and served under that commander during Hood's Tennessee Campaign.
The rolls and other records in service files should offer some indication as to where they were taken.