Whether these people had celtic culture at that time or acquired it later is open to conjecture.

As a matter of fact, it's not. There was a thriving Celtic culture in North-western Spain (just like there was one in Brittany in France).

The article saying

Don't tell the locals, but the hordes of British holidaymakers who visited Spain this summer were, in fact, returning to their ancestral home.

...

DNA analysis reveals they have an almost identical genetic "fingerprint" to the inhabitants of coastal regions of Spain, whose own ancestors migrated north between 4,000 and 5,000BC.

and talking about generic "coastal regions" makes it sound like the Celts come from Benidorm. They are found in the Spanish Northwest, in Galicia. I am, in fact, not aware of Celtic archaeological remains anywhere else.

Those whom the Gods wish to destroy They first make mad. — Euripides