It was not a Roman province fully. The Roman Empire was ruled by several Arab emperors.
Even after Islam the Byzantine Empire was ruled by Arab emperors and dynasties also.
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It was ruled by local Arab kingdoms and even empires as well and jointly.
Palmyrene empire
en.wikipedia.org
and the Arab Ghassanids that ruled it for 400 years.
en.wikipedia.org
Arabs also ruled several kingdoms in Syria before the Roman Empire even was created.
Arabs/Semites are native to all of the Levant, the Europeans (Romans) were foreigners in comparison. This is why their rule and presence was only temporary.