Two main reasons come to mind about why your ancestors might have enlisted in 1863.

First their home state of Arkansas was being invaded by whta was to them a foriegn army.

Second; The Conscription (Draft) Act of April 1862 which required that all males over the age of 17 be enlisted in the Army unless they were otherwise exempted from such service.

There was no such thing as picking your side if you were a resident of a southern state you were expected to serve in the Confederate army. The same was true in the northern states. Conscript Officers on both sides regularly made their rounds to enlist those who had deserted or were otherwise trying to avoid their military service.