Turin was (and to an extent, still is) the industrial heartland of Italy, so it's easy to guess why they would be more prone to voting communist (and their successors, in theory at least).
The Communists did a good job organizing the Southern Migrants in the Turin agglomeration; better than at Milan. The grandparents (and for those above a certain age, parents. And for those above another certain age, they themselves) of the vast majority of the inhabitants of Turin's banlieue are Southern born.
Yes, Basilicata took a massive leftward swing with the end of the First Republic, although it (along with Molise) had always been voting somewhat to the left of the more populated parts of the Mezzogiorno even before that.
