"mass movement of Turks into central Anatolia" is an unsourced statement from a Wiki article, so I am not sure if it's worth discussing (the article I cited above disputes that). If there was a massive wave of newcomers there should be genetic evidence. Also considering the Byzantine Empire of the Comnens (12th century) covered about half of Anatolia, I doubt "the biggest areal [Turkish] language spread happened from 11th to 14th in the Anatolian area". 

I don't think "critical mass" is a meaningful concept here. As Don Ringe put it: "History shows that comparatively small groups of immigrants can induce their new neighbors to adopt their language — gradually over several generations, of course — if (1) they have enough economic or political power, and (2) they can offer some important advantage to those who are willing to adopt their language." So it's not just a question of numbers. (of course there are some speakers - someone has to speak the new language first)