I think he did have these abilities at such a young age. Might sound ridiculous I guess but Octavian was a very cold, calculating person from the outset. His method of how he would hold power (Caesar himself had sorted out his achieving the power) meant that he had to rely on his own inherent abilities. They might not have been refined but his idea of how he would govern was there before Actium. Also, we have to assume that Caesar knew what he was doing in choosing this young man.
As for maturity, given that Roman society did put so much emphasis on maturity, he had to have some inbuilt mechanism to survive. Which must have contributed to him achieving the consulship at 20 instead of the given 42? Apart from the blackmail element.
Being aware of the maturity aspect, perhaps he tried to make himself seem not so much a daddy in years but in stature. Obviously, he couldn't be the adventurer or showman that Caesar was or the General that Antony was and therefore had to choose more subtle means of control. Perhaps it was the abilities portrayed at such a young age that made Agrippa stick with him so early on?