I’m no lawyer but it seems the Confederate Constitution went the extra step.
Yes they did. Obviously they concluded that Article IV, section II was not clear enough because pretty much every state ignored it (thanks to Justice Story in Prigg v Pennsylvania) and in a manner of speaking, this is exactly what caused much of the friction between the North and the South.
Spelling it out explicitly and numerous times throughout the document was probably their way of trying to make certain that no future Liberal Judges can change it on a whim or through "creative interpretation."