Cindy: I do not find a record for John Ulman in a Missouri Confederate regiment in the list maintained by the National Archives.

Perhaps one of these men that served in the Missouri State Guard is your man:

J. M. Ullman, 3rd Lt, Co A (Osage Tigers). 1st Cavalry Regiment, 6th Division.

J. C. F. Ulman. Pvt, Co A (Osage Tigers), 1st Cavalry Regiment, 6th Division.

Unfortunately, the Osage Tigers appears to be a Miller County company.