It's a bit hard to answer your question, because the answer changed over time. The Roman province of Africa was first occupied by Rome after the Third Punic War. During the Punic Wars, Africa was the site of the city of Carthage, which was the seat of a sizeable empire of its own, and one which fought bitter wars against Rome and very nearly brought her to ruin. During this period, of course, Rome clearly saw the Punic and Berber peoples inhabiting the area as both foreign and hostile, although they were willing to work with some of them against Carthage. At this time Rome still saw even a lot of Italy as "foreign," (although certainly more closely akin than Punic Africans), and a war would be fought between Rome and other Italian nations, principally over the issue of whether the other Italians (the socii or allies) would get to be Roman citizens or not.

But, as in Italy, in Gaul, and in many other places, what was seized by the sword was ultimately retained by coin and colonization. Africa was economically important as a source of the grain that supplied the gigantic urban population of Rome with bread, and many Romans set up successful business ventures there. Additionally, a custom developed in the 1st century BC that retired or discharged soldiers would be given plots of land as a reward for their service, and Africa was a popular destination for this. There were several advantages to this. First, discharged soldiers were seen as a problem demographic for various reasons, and sending them far away from Rome was seen as safer than having them nearby. Second, these men would bring the Latin language and Roman culture to Africa. Third, these were still trained soldiers, and although this made them dangerous to have in Italy, it also made them useful to have in foreign parts, as they could be rapidly mobilized to meet any sudden security threat.

Over the next several centuries, the Romanization process was overwhelmingly successful, to the point that in AD 191, Septimius Severus, a prominent general and Senator of mixed Italian and Punic ancestry, who was raised at Leptis Magna and who spoke both Latin and Punic flawlessly, fought off all comers and rose to become Emperor. Severus was in touch with his Punic heritage, to the extent that, while campaigning in the east, he actually dared to pretty up the tomb of Hannibal, the Punic leader who, of all her enemies, may be said to have come the nearest to destroying Rome.

By this time it was quite clear that the province of Africa was integral Roman territory, and although ordinary Romans might well have gawked or sneered at the strange mannerisms of provincials, it was more a matter of city folk and the hicks from the sticks than any question of being "foreign."

By the time of Theodosius, it has been assessed that the area of Old Carthage (now part that part of Tunisia facing Sicily) was one-third Latin by ancestry, and almost all the rest spoke Latin fluently. Substantially everyone was by then a Christian, which had become another mark of "Roman-ness."

Carthage and its hinterland were conquered by the Vandals in the 5th century, but were eventually reconquered and remained part of the Byzantine Empire after the collapse of the Romans in the west. It was not until 698 that the region, by then called the "exarchate of Africa" was permanently separated from Roman or Byzantine influence, when the Umayyad Caliphate attempted to deliberately destroy the city and depopulate the area to prevent the Byzantines from reconquering it. The area was heavily damaged, and although some people were still there and it remained to some extent Christian (there was a Bishop of Carthage until at least 1076), Africa Province's time as part of any European polity were over.