According to Pontius' Life of Cyprian, Jerome's source of information, Cyprian assumed the office of a presbyter very shortly after his baptism in 245, seemingly without ever being ordained to lower clerical grades (see ). The Life of Cyprian also tells about the friendship between Cyprian and the presbyter Caecilius of Carthage, and suggests that Caecilius adopted Cyprian, or at least made him his heir, see . This could explain Jerome's remark concerning Cyprian's cognonmen. Cyprian was elected bishop of Carthage some three years later in 248/249.
On the Life of Cyprian, see Robert Wiśniewski, Cult of Saints, E00916 - http://csla.history.ox.ac.uk/record.php?recid=E00916