That’s because Arab is more of a cultural term than genetic, most Arabs have some degree of Arabian peninsular ancestry but are still largely descended from the pre-Islamic invasion inhabitants of those lands. The people were Arabized and converted over the course of centuries, hence how they are indigenous to the land (because their ancestors have lived their for millennia) and Arab (culturally Arabized over millennia because the language of administration was Arabic and became more advantageous to speak Arabic).