Philip was the son of a Roman citizen born in Arabia Petraea (today bits of Jordan, the Sinai, and the southeastern Levant). This doesn't mean that he was not an Arab, for one technically speaking all free men of the empire were granted citizenship in 212, but more to the point the ethnic make up of the Roman citizen body was fairly diverse by 200 CE. "Citizenship" was a statement of affiliation and socio-political privilege rather than of ethnic group identification, there was no contradiction between being a Greek, a Gaul, an African, etc and being a Roman. In his Discourse to the Romans, the Greek orator Aelius Aristides (who was a Roman citizen) said "You have divided into two parts all men throughout your empire... everywhere giving citizenship to all those who are more accomplished, noble, and powerful, even as they retain their native-born identities" which I think gives a good idea of how "Romanness" operated.

As I flipped through the (very scanty) sources however it is interesting to note that they all universally condemn Philip's background, saying he was of ignoble birth, and the Epitome De Caesaribus even claims that his father was a "most leader of bandits". Latro, the word for bandit, has a really complicated and tricky use in Latin and in imperial discourse, so it is hard to know what to make of it. It is possible that this only means he was a prominent local leader, and the author is basically dismissing the Arabians as all bandits.