The group you're referring to are the Arbëreshë. The Arbëreshë represent an early Ottoman-era migration. During the spread of the Ottoman empire, a large number of Albanians fled the Balkans and landed in southern Italy.

The Greek population migrated slightly earlier. However it's significant that, in terms of the modern nation states: They share a border, borders are porous, and borders in the region have been shifting throughout history.

The area that was inhabited by Albanian-speaking peoples in the Balkans is and was much much larger than the current boundaries of the modern Republic of Albania. Kosovo, parts of Montenegro, large parts of Macedonia, in addition to what you've seen of Greece and Italy, all have large Albanian populations. It's kinda like the saying about Spanish speakers in California: They didn't cross the border; the border crossed them.

The Balkans, in general, are hugely diverse, everywhere in the area has a good mix of people of different backgrounds. There are also villages in modern Albania which speak Greek, for example.

Another important thing to remember is that the area we're talking about is really quite small. If you look at a map of the Great Lakes area, Albania is about the size of the Massachusetts. Migration, while hindered by the mountainous terrain of the area, is not that unfathomable considering the small scale of the coastal Balkans.