At the time, yes, although in official correspondence it was more often Rebels than anything else. The terms "secessionists" or "traitors" are seen most often in the press or political rhetoric The original question seemed to ask what we today would refer to them as, not the parties at the time.

As for Joe Wheeler, of course his appointment was symbolic of the reconcilliation that the nation was undergoing. In addition, he was a a nine term member of Congress who strove to foster the healing between the north and south that was going on during that period who had commanded large numbers of men and written books on cavalry drill and tactics. He volunteered for duty and, being probably the most famous Civil War veteran still capable of serving, was appointment Major General of Volunteers in command of the Cavalry Division, not the whole army. Interestingly, his second in command who took over the division after Wheeler was laid low with illness, was Samuel Sumner, a Union veteran who had served on the staff of his father Edwin Sumner.