I don't see any reason to suppose that the author of Acts made up the "of Tarsus" but rather that Paul was from Tarsus. Whether he was educated there and in Jerusalem is a guess, but it is certainly a possibility. However, the knowledge of (and the fact that Paul refers to it in the way he does) his tribal lineage, his cirumcision, his use of Kephas rather than Petros, his knowledge of aramaic, his "zeal", and other signs all point to a devout jewish upbringing and education. Yet Paul also seems to follow the LXX, and although he probably dictated, rather than wrote, his letters, he still dictated in Greek, and I find it unlikely that this was a learned language but rather his primary language (perhaps he was raised speaking aramaic as well as Greek, perhaps he learned it later). I would say he was born in Tarsus, raised there, and perhaps sent (or travelled) to Jerusalem for additional education (especially if he really was a pharisee).