From the records that exist, here, in my opinion, is the most likely scenario regarding Jesse Russell of Pike County, Mississippi:

1. According to the individual who wrote up the bio on FindAGrave, Jesse Russell was born in Pike County 10 Aug 1823. This information somewhat parallels the following:
2. The 1850 census of Pike County, Mississippi, shows Jesse Russel - age 24, and
3. The 1870 census of Sabine Parrish, Louisiana, show Jesse Russell - age 48. (It is common for ages to be off by a few or sometimes several years).
4. The Confederate Conscription Act of April 1862, set the draft age from 18 to 35. In September of that year, the upper limit was raised to 45. In Feb. 1864, all men from 17 to 50 were called.
5. The muster rolls for Company C, 32nd Mississippi, are, for the most part, complete from the original muster-in in March 1862, through April 1864. March-April 1864 is the last muster roll on records for that company.
6. The only records we know of for this man as a member of Company C, 32nd Mississippi, were not Confederate records, but were Union Army records of the Army of the Ohio, listing him as a prisoner of war, deserter, and of him, on Dec. 6, 1864, taking the "oath" (of allegiance to the US) to remain north of the Ohio River for the duration of the war.

In March 1862, Jesse Russell was somewhere between 36 and 40 years old. He was not subject to the Conscription Act. In September 1862, he became subject to the act, and therefore could have enlisted or been drafted. Muster rolls of the company up until the last record in April 1864, do not show him with the company.

Given the facts that we know, there is a likelihood that Jesse Russell was conscripted into Confederate service probably in early 1864. If he was, he would not have necessarily been given the opportunity to enlist or serve with a company from his home county. He also would not have gone to Tishomingo County to "enlist". The company had long since left that county. Once conscripted, he may or may not have gone to a Camp of Instruction. In either case, he would have been assigned to a company based on manpower needs, without regard to where he was from. It is impossible to know the circumstances of his desertion, however, it had nothing to do with Vicksburg, as his unit was not there during the siege and surrender; and in July 1863, it appears that he was not in the Confederate Army. One other thing we can only speculate about is his reason for relocating to Louisiana after the war. We do know that many men who took the oath prior to the war's end felt it best to find another place to live afterward, some even choosing to stay "north of the Ohio".