If this question refers to Julius Caesar, he was not an emperor. Rule by an emperor in Rome started with Augustus, 17 years after Caesar’s assassination.
In 63 BC Pompey turned Judea into a client state when he intervened in a civil war between the sons of Salome Alexandra, the queen of Judea. He put one of the sons, Hyrcanus II in charge. He was succeed by Antipas, a courtier. His son Herod the Great was designated king by the senate in 40 BC. After his death, the kingdom of Israel was divided among his sons who became tertrarchs (rulers of a quarter). From then on, Israel remained divided.
In 6 BC Judea was annexed to the empire. it was ruled directly by the Romans. It became a satellite of the Roman province of Syria. It came under rule of the governor of Syria who sent an official (prefect) to administer it. These were the two heads of government and the men who reported to the emperor.
From 41 to 44 AD Judea was allowed nominal autonomy and Herod Agrippa was made king of the Jews. It briefly returned under direct Roman rule. Agrippa II became the 7th Herodian king of the Jews from 48 93 AD. then, due to rebellions, Judea became a separate province with a governor because governors could be in charge of legions and able of directing military suppression of revolts.

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