Historical Context
The Valerian persecution (253-260) targeted Christian clergy in particular, and the bishop of Alexandria, Saint Dionysius (bishop c. 247-264/265), was among the most prominent leaders arrested and exiled. Because these four served as deacons directly attached to Dionysius, they were swept up in the same proceedings against the Alexandrian church.
The persecution eased only after the Emperor Gallienus released prisoners and permitted the churches to reopen. The severity directed at church leadership explains why deacons in immediate service to the bishop would be arrested and banished together with him.