Dr. Temple is mistaken. William Temple and Francis Marion Temple served in the Union, not the Confederate army. Capt. James F. Allison, whom he alluded to, commanded Co. D, 1st Arkansas Cavalry, U.S. Volunteers.
There's no record of either of the Temple brothers ever serving in the Confederate army.
Dr. Temple may simply be unaware that Arkansas, a southern state, furnished several regiments of Union volunteers. That's a common mistake.