Was Roman imperialism offensive or defensive after the Punic War?

Answer 1

If you mean after the Third Punic War, when Carthage was completely eliminated, it was neither defensive or offensive.

By its intrusions into Spain, North Africa, Greece and Asia Minor, Rome had become irretrievably engaged in those areas, having imposed settlements and established tributes which it had to uphold. Also, kingdoms and cities turned to Rome for help when in trouble with neighbours. Conquering Roman generals had an obligation to the cities and states they had conquered as their patrons (the conquered had become their clients, and they were obliged to look after their welfare). And those states sent embassies and gifts to Rome seeking justice and retribution. Rome had made itself a powerful intervener.

So whether Rome wanted to expand or stabilise, the activities both within the areas where they had imposed settlements, and on the borders where intrusions came form outsiders, meant that Rome had little option to play protector, pacifier and punisher. And it was of course in Rome's interest to promote stability to ensure the taxes/tribute rolled in. Rome had become hooked on this foreign wealth and food supply.