Areas ethnically cleansed of Armenians during WWI were generally settled by Muslim refugees fleeing former Ottoman territories in the Balkans, Caucasus, and so on. Some of these refugees were Turkish-speaking but others, such as Circassians, were not. Even before WWI, the Ottoman government had a policy of settling Muslim refugees in Anatolian land formerly inhabited by Greek and Armenian Christians. Muslim refugees were also settled in places such as Jordan. Eugene Rogan mentions this issue in The Fall of the Ottomans. For example:
"In February 1915, the Ottomans began to deport Armenians from Dörtyol and Alexandretta (in Turkish, Iskenderun) to the Adana region. On the model of the Greek population exchanges, Muslim refugees were then resettled in the forcibly vacated Armenian properties."^1
In the post-war years, many of these areas were resettled by Greek muslims as a part of the population exchange between the two nations. As an effort to create further religious homogeneity in Turkey, the CUP agreed to send Orthodox Christians and remaining Armenians to Greece. Because there were fewer Christian Turks who were sent to Greece than Muslims who were sent to Turkey, there was a reasonable amount of land for them to settle on. Even with this, there were many accounts of a struggle to fully integrate within Turkish society as many of the Greek imports did not speak Turkish and did not feel a part of the society as a whole.
Most of what I know on this comes from Bruce Clark's "Twice a Stranger: The Mass Expulsions that Forged Modern Greece and Turkey" while Eugene Rogan's "Fall of the Ottoman's" to give good information on the period in general. I'll see if I can get a hold of Twice a Stranger tonight because I think that could be helpful