Yes, the Southern states did lag behind the Northern states in the adoption of the ideas of the penitentiary movement. Historians typically argue that the reason for this was rooted in the South’s political culture.
Southerners typically opposed the creation of penitentiaries. They were more inclined to support traditional punishments such as public corporal punishment. Historians believe that this came about because of the slave system in the South and the definition of freedom that it engendered. However, there is no objective way to prove this.
The argument is that Southern whites were particularly attached to the idea of personal freedom because they saw how horrible it would be to be a slave. Therefore, they did not trust authorities that tried to claim control over them. The penitentiary was seen as such a claim. It was a claim that the government had the right to take white people (criminals though they were), put them in one place and exert complete control over them. This seemed wrong to whites in the South in that it seemed to be too much like slavery.
The penitentiary movement in the South did lag behind the North, with some historians theorizing that this lag was caused by the political culture of the South.