Alexander was the son of a religous and rich man from Egypt, and he was related to the philosopher Philo of Alexandria. He crucified two men, James and Simon, who were sons of the Judas who had revolted against Cumanus and Cyrenius' taxation, for unknown reasons. He also imported grain from Egypt because of a great famine in the province. Other than these incidents, Josephus notes that Alexander's reign was a tranquil one.

Ancient sources: Antiquities 20.5.2; War 2.11.6, 2.12.1, 2.15.1, 2.18.7-8, 4.10.6, 5.1.6, 5.5.3, 5.12.2, 6.4.3; Histories 1.11, 2.74, 2.79; Suetonius, Vespasian 6.