I was under the impression they were from Syria.
It was ruled AS part of North Africa, but it was ruled (though weakly) by Syrians (largely semitic at the time)
If the Berbers were indigenous, then they weren't originally related to the Vandals, who were a Germanic tribe that entered North Africa via Spain.
The Iberians were not Celtic, but were rather a North African people who crossed the Strait of Gibraltar around 1500 BCE. The Basques seem to have already been living in the Pyrenees at the time. Celts migrated into northern Spain around 700 BCE via France, and the Celts and Iberians eventually merged. In the meantime, Phoenicians and Greeks settled a number of trading colonies along Spain's Mediterranean coast (with the Phoenicians eventually being replaced by Carthaginians). As elsewhere around the Mediterranean, there was a lot of mixing of peoples.