The Ottomans use the northern European mill model, it would be correct for them to use the Mediterranean mill model that was added with the Byzantines. This is due to the fact that the Ottomans arose in Anatolia and inhabited it for centuries.
Also, when they add Spain and Portugal in the future, they should give them the Mediterranean mill model.
Reference images:
Northern European mill.
Mediterranean mill.
Ottoman origin in Anatolia.