No, it will not show up because you were not arrested or criminally charged. The stores are now imposing their own "civil fine" which is actually nothing of the sort. It is just their way of scaring people and doing their best to stop shoplifting. Hopefully it scared you enough that you'll never do that again, no matter how easy it appears at the time. Also, hopefully you get that corrections job and will make plenty of money and never feel the need to steal again.
Since you were never arrested, this incident should not show up in a background check. I would advise tou that if you receive a letter from a law firm seeking to collect money on that "civil demand," consult with an attorney. Those letters scare you into sending money and you should not have to. Feel free to contact me if you would like me to review the letter and respond to it on your behalf. Or you could simply wait until (or if) you even get any follow-up correspondence.
Meanwhile, good luck with DOC!