That is the ancient Irish legend but the fact is that northern Spain and Ireland were simply the northern and western extents of the Celtic world prior to the Roman conquests.
There was no need to sail from northern Spain to Ireland to explain a common genetic stock. The Celts expanded from Gaul to Hispania and from Gaul to Britannia to Ireland.
So, if you travel to Galicia (from the Roman term "Land of the Celts") and Asturias in northern Spain, you won't find locals playing castanets and guitars or any flamenco dancers but you will find the locals playing bagpipes. In case you are interested: The Celtic Music of Spain -- Galicia & Asturias
Prior to the Roman conquest, this was the geographic extent of the Celtic world:
During the Hellenistic times, Celtic invaders reached Anatolia (what is now Turkey) -- as depicted in the Hellenistic statue "Dying Gaul" -- and settled there giving rise to the Galatians. That would also account for a DNA match to "Turkey".
For these DNA tests to be informative, they should give out the rersults of ancient ancestral root results by referring to "Celtic" or "Slavic" or "Arab" or "Sub-Saharan". Describing a genetic makeup as "Spanish" or "Turkish" is as meaningless as describing a genetic make up as "New Yorker".