The camps back east were in charge of a camp commander, who was permanently assigned to that post. The camp did not house any "tenant" combat troops, but there were men detailed from line regiments and staff departments who worked for the camp commander as hospital attendants, cooks, clerks, etc. The camps had quartermaster, commissary and medical facilities. The paroled troops, of course, were not permitted to perform duties that benefitted the war effort, so they were kept busy doing fatigue duty around the camp and serving as provost guards to keep order within the camp. There was a liberal furlough policy. From everything I've read, the Confederacy strictly honored the parole/exchange rules and agreements.
Throughout the war there was a continual series of meetings between U.S. and C.S. civil and military negotiators who worked out agreements and conditions for exchange of prisoners. The Southern Historical Society Papers reprinted hundreds of pages of transcripts of the negotiations. It makes fascinating reading. The exchange commissioners decided through negotiation and agreement on when the paroled troops would be formally declared exchanged. Notification of the exchange agreements were promulgated, on the Confederate side, by general orders from the Office of the Adjutant and Inspector-General. Once the general order was received at the parole camp, the troops were free to take up arms again.