Is there any evidence that the Phoenicians were originally from Iberia (Spain)?
Nope, none. The Semitic Phoenicians came from the general area of the eastern Med and/or Middle East, and there's some speculation (which I believe dates to ancient times) that they originally lived south of the Sinai.
In Iberia there was a so-called Tartessian culture, apparently prehistoric (iow, no writing, or none that has survived), that antedates Carthaginian colonization, the latter of which was pretty rapid. The Celtiberians were also a drift that made up pre-Roman Iberia.
Also, contrary to the usual claims, there's little evidence that the Basques were there until late antiquity or early middle ages, and a language isolate arriving after the breakdown of the Roman Empire in the west does make the most sense.
The Tyrians (Phoenicians of Tyre) were the settlers of Carthage. The earliest date that has been established for the settlement of Carthage is 8th c BC.
The former Portugeuse holding of Mogador, on the western coast of Africa, is one of the settlements described in the Periplus of Hanno, which describes a voyage and colonization from Carthage, outside the Pillars of Hercules, and a bit deeper to the south than the clearly described active volcano now known as Mount Cameroon. Phoenician pottery frags of the 7th c BC (at least one with the personal name "Mago" on it) have been excavated there.
Herodotus describes the Phoenician circumnavigation of Africa starting from the Red Sea, and contracted by an Egyptian pharaoh.