P.Zanker’s The Power of Images in the Age of Augustus (2014) (pp. 51-3) - “The relationship with Apollo would prove to be ideally suited to Octavian himself and to furthering his political image. All these goals and objectives, both during the struggle with Antony and then later in the building of a new order, could be associated with the God. Apollo stood first for purification and for punishment of any form of excess. As such he could well represent Italy’s position during the civil war with Antony, with the motto ‘Italy versus the Orient with its luxuria, against Egypt with its animal-headed gods and its decadence’. But after the victory was won, then Apollo took on his role as singer, lyre player, and god of peace and reconciliation. As the prophetic god, with sibyl and Sphinx, it was he who proclaimed the long-awaited new age.”
Octavian took advantage of Apollo’s multi-faceted nature in establishing his public image - "furthering political image"
During TRIUMVIRAL PERIOD, Apollo represented discipline and morality - counterpoint to Antony’s Dionysus
After Antony’s defeat, this became less relevant, and so he began to focus on other aspects of the god.