Pre-1453 and Post-1453 policy.
Before 1453, Christians were given the status of Christians anywhere in Islamdom as dhimmis, and were subject to missionary activity, as described in Nick Nicholas’ answer to When and how did modern Turkish become the majority in Anatolia?.
Even so, intense conversion of Christians to Islam in Anatolia only happened in the 14th and 15th centuries, and presumably is to be associated with the more fervent Islam of the Turkish emirates, rather than the stability of the preceding Seljuk Sultanate. Just because you’re conquered by Muslims doesn’t mean there is immediate pressure for you to convert. For a parallel, see the Copts of Egypt; I learned (from Dimitris Almyrantis, I think) that the mass conversions to Islam only date from the 10th century.
After the conquest of Constantinople, the Rum Millet was instituted by Mehmed II, which afforded Christians in the Ottoman Empire a good deal more autonomy, and less pressure to convert. Accordingly, there was not actually that much missionary activity in the Balkans, or for that matter in the Rûm Eyalet (the Pontus, which was conquered only after the Rum Millet was established). The Muslim indigenous populations in the Balkans (Albanians, Bosniaks) and in the Pontus (Greek-speaking Muslims) resulted from deliberate missionary activity in the 16th and 17th centuries, and they had limited scope. (See e.g. Islamization of Albania)