"it states he served under "Generals" Cooper, Kirby, Smith, Harrison, Heinman..."

Brig. Gen. Douglas Hancock Cooper - commander primarily in Indian Territory
General Edmund Kirby Smith - Brigade Commander in Army of Northern Virginia, Division and Corps Commander in Confederate Army of Tennessee, finally Commander of the Trans-Mississippi Department
Harrison - probably Brig. James E. Harrison of Texas or his brother Brig. Gen. Thomas Harrison
Heinman - Major General Thomas Carmichael Hindman commanded a division in the Army of Mississippi (at Shiloh), then commanded all troops in Arkansas, North Louisiana and Indian Territory. Ultimately sent east to command a division in the Confederate Army of Tennessee.

The 1st Missouri Cavalry Regiment (CS)never served under any of these generals.

I'm puzzled!

Jim