Lieutenant Colonel William M. Lowe arrived at Fort Delaware from Point Lookout on 28 APR 1865 and was released on special orders from General U. S. Grant. He was released after posting a $2,000 bond promising to remain faithful to the Oath of Allegiance which he had taken the day before. The bond is dated 7 JUN 1865. This special release suggests that Lowe asked to take the Oath of Allegiance before President Johnson's amnesty plan was proclaimed on 29 MAY 1865, and perhaps after the Citronelle surrender on 4 MAY 1865 was announced to the prisoners. The language of the Oath was repeated in the handwritten bond signed by William M. Lowe and sworn to in the presence of Captain George W. Ahl who was in charge of prison operations at Fort Delaware. This posting of a bond to insure faithfulness to the Oath is unusual in the Fort Delaware release records that I have examined.
Your observation that the 13th Alabama Cavalry was never officially enrolled in Confederate service may have had something to do with this bonding to remain faithful to the Oath of Allegiance. But I'm not sure how the Federal War Department would have known that.
Of further interest is the information that he ran against "Fightin Joe" Wheeler for the U. S. Senate in the post war years and won. Major General Joseph Wheeler arrived at Fort Delaware on 22 MAY 1865 and was released on parole on 8 JUN 1865. Wheeler's release on parole without being required to ask for a Presidential Pardon and take the Amnesty Oath resulted from the Federal War Department's recognition of his status when detained in Georgia as a paroled prisoner of war under the Greensboro, North Carolina agreement dated 26 APR 1865. Lowe and Wheeler may have known each other before the war, but they were not likely to have met during Wheeler's brief stay at Fort Delaware, although Lowe would have known through the grapevine that General Wheeler was there. Colonel Lowe was housed out in the officers pen in Division 39 out on Pea Patch Island. As a high ranking political detainee, General Wheeler was kept in close confinement inside the Fort.