You're right about him not using the exact same title; he went with Imperator, which used to be reserved for generals whose victories rated a triumph. Still, the custom - although in disuse - was there to be tapped into. Augustus could claim, plausibly, to have brought an end to the civil wars that had rent the late Republic.
Octavian was not very good at winning battles (but good at getting others to win them for him), but had superior political skills. He had to avoid antagonizing the old senatorial families, but at the same time he needed to reassure the common people that he would remain in control. They didn't want a return to the free Republic which would mean more civil wars. So he had to work out a system by trial and error, pretending to "restore the Republic" while making sure he had the essentials of power. Having most of the legions under his command was a major component of his power. It was a military despotism but disguised in order to make it acceptable to the senatorial elite.