Paroled soldiers stayed in camps under military discipline, but in their own territory. One such camp was located somewhere near Mobile. One of my ancestors spent some time there after being captured and paroled at Vicksburg. Don't know exactly how long.
After the exchanges were made on paper, the authorities issued orders to the individual soldiers to return to their units.
In theory no one was supposed to go back before they were exchanged, but the South was accused of doing it.
Fred