He wasn't busted to colonel. He requested it.
"Pemberton resigned his lieutenant generalcy and requested assignment as a lieutenant colonel of artillery. He had suggested such a possibility in conversation with Bragg during his visit with Davis to Bragg's army. Bragg, when asked for his comments on Pemberton's situation, had informed Davis of Pemberton's wishes. So this action was no doubt taken as a result of a prior understanding with Davis and the War Department. This humble act, especially humble given the pride of Pemberton, quieted some of his critics and gave him what he had always preferred: a command in his beloved Virginia."
- Ballard