I did a quick look. The record that shows Jacob was in the 12th TN comes from Ancestry and the source says it originated in an article in Confederate Veteran, which seems to have been based on records from the cemetery associated with Camp Morton. The Confederate records online, however, show Jacob was actually in the 47th TN, Company B. He enlisted December 8, 1861 in Gibson County, joining Company B. The notes on the May/June 1862 muster roll say he deserted May 10, 1862. But the notes on the July/August 1862 muster roll say he deserted June 1, 1862 at Corinth.
The next set of records show Jacob back in the 47th, this time in Company H. He shows up on a POW list which says he was captured near Chattahoochee, GA July 4, 1864. He was sent after his capture to Nashville, then Louisville, then on July 13, 1864, he was transferred to Camp Morton in Indiana. The records show he died at Camp Morton March 11, 1865, from an inflammation of the brain. He was buried in the Green Lawn Cemetery. Those graves were relocated in the 1930s to the Crown Hill Cemetery - Jacob is listed on FindaGrave as being one of the persons known to have been buried at Green Lawn who may be among the bodies relocated. The plaque with his name has the 12thTN on it so I'm assuming that is where the incorrect record came from.
Now - the first set of records which show Jacob joining and deserting come from CSA records. The second set are all Union and all created as Jacob went through the Federal prison system. But how did Jacob get back in the 47th? There is another set of records for a Jacob Blessing from Tennessee - serving in the 15th TN Cavalry, Company A. This Jacob joined December 1, 1863 at Eaton, TN. Eaton is in Gibson County - is this the same man? The only record this Jacob has is a muster roll from May 11, 1864 when he was marked present. If this is the same man, he would not have been the first to leave the infantry and rejoin a cavalry unit later.
As to conditions at Camp Morton, they were poor. There are a number of books and articles you can read about how prisoners were treated during the Civil War - it's not pretty on either side. I suggest you take a look at the forum on Prisons and Prisoners - there are a number of good threads in there.
https://civilwartalk.com/forums/prisons-prisoners.292/
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