I can't imagine Iberia being controlled by a European power. it was pretty isolated from the rest of Europe by the Pyrenees and the western Mediterranean. It makes more sense for a regime to rule it from across Gibraltar. Iberia has just always been culturally part of Northern Africa, and I can't imagine a Europeanized Iberia.
Gibraltar? You mean the Gate of Gades, certainly. I've never heard of this "Gibr" or any altar to him in history or regional mythology.
As for being culturally Punicized, though, I'd argue the that only naturally applies to the coast along the south and east as a matter of course. Prior to their slow integration into the Barca political system the tribal groups and early polities of the central platue had far more in common with the Celtic groups than the Phoenician or Tuareg cultures. Keep them isolated behind those ranges and out of North African influence during their period of full settlement and consolidation and like as not they'd develop into a distinct set of groups that are neither Celtic, Punic or Helleo-Latin.