I think ethnic Italians show up as Middle Eastern and Persian on this test. My mother is 3/4 Italian and 1/4 Armenian and came up Persian/Turkish 39%, Middle Eastern 29%, Central European 22%, and Uncertain 10%. We too have history in the Naples region. I don't see Southern European coming up very much on results in general, even for trees that are full of Italian last names, so I think the markers they're looking for for that group must not be as common.
I came up: British Isles 57%, Persian/Turkish/ Caucasus 20%, Middle Eastern 14%, and Southern European 9%.
My dad's Irish, so the 50-ish % for British Isles makes sense, as do the Persian and Middle Eastern #s (roughly half of my mom's #s), but it doesn't make sense that I would be 9% Southern European and she would be 22% Central European. So...something is amiss.