Your post contains some curious information. What is your source?
Information on Indian Units is incomplete, especially in the latter years of the war.
I cannot find a Capt Thomas Miller in the Confederate Indian Units. In particular, I do not find anyone named Miller in the 1st Chickasaw Infantry.
Tahlequah is the capital of the Cherokee Nation. By Sept 20, 1863, Tahlequah and all the Cherokee Nation for that matter is "behind enemy lines", though the Confederates are very active in scouting and raiding through the Nation.
Pvt H. George was enrolled and mustered in on Sept 20, 1863 in the Creek Nation in Gregg's Company, Capt. Thaddeus Gregg. The regiment was also known as Hunter's Regiment Indian Volunteers, Col. Wm L Hunter commanding.
I'm quite curious as to your source of him enlisting at Tahlequah and in the name Capt Thomas Miller. Perhaps there are some clues that fill in some gaps on the sparce records of Indian Territory units.