I got asked a question some time ago: Why doesn't Albania have an Ottoman Turkish minority? When I first read it I was also surprised and then, it looked like there was some sort of Turkish removal in Albania. I had to ask also a good friend of mine, who has studied history, Stivi Kotroçi just to be sure about this. With the history books of the Balkans you can never be 100% sure.
It turns out modern day Albania was not so interesting for serious migration of Turkish communities, it was a remote area, filled with swamps with no special incentive. What happened is the opposite, many Albanians migrated towards the places like Istanbul, 28 Viziers of Albanian roots in the empire, in ~400 years: Albanian Grand Viziers of the Ottoman Empire. Of course, the people migrating during the people didn't all pursue political enlightenment, but I mention this as an example.
Also, the Vilayet of Kosovo was far more important than Shkodra and Manastir, situated in the middle of the Balkans. You’d expect people migrating to [cool-area] and not [next-to-cool-area-that-is-not-cool] in larger waves, no? These were the three political regions where Albanians were ethnic to.
Now, as Albania, Bulgaria, Greece, Montenegro, Romania, and Serbia established their nation states and embarked on their policies of creating homogeneous ethnic societies, Turks and non-Turkish Muslims (e.g., Cretan Muslims, Pomaks, Roma, Torbesh, and Vallahades) of the region began to search for new homes in the Anatolian peninsula (Duman 2008, p. 23; İpek 1999, pp. 14–21; Todorova 1997, pp. 348–349). This was a rather new migration flow: instead of the historical East to West migrations of the Turks to the newly conquered Ottoman territories, this migration was from the West to the East—this time from the lost lands to the safe haven of Anatolia. It was in this context that the Greek revolt was accompanied by the slaughter of many Muslims and the flight of many others (McCarthy 1995). Most of these refugees went just northwards to a part of the Balkans still under Ottoman control rather than to what is now Turkey. Many of them, however, undoubtedly migrated to Turkey at a later stage. - Taken from: The Changing Waves of Migration from the Balkans to Turkey: A Historical Account
Pictured above, you can see again, modern day Albania, Albanian migrations, old timer Kosovo, Turkish migrations.
Something else worth noting, there is no record of any forced migration of Muslims or Christians from Albanian land, unlike Greece, Serbia and Bulgaria. So the idea of any type of cleansing doesn’t really hold up. See: Bulgarian Turks and Persecution of Ottoman Muslims.
After 1913, when the European powers agreed on the borders of Albania, which Albania contested (I wonder why: Kosovo / F.Y.R.O.M / ~Greece) it so happened that those former cool cities to go-to for Turkish people where outside Albania. Then the swamps were dried, and one of the greatest regional changes was that of Myzeqe, basically the region that enjoys the most modern lifestyle in Albania.