When my husband, son and daughter in law went to the Oykun they were all in the same room for the Turkish Baths. There was no separate place for woman and men. This was 3 years ago, so it may have changed since then.
As I did not want a Turkish Bath. I opted for a facial. I was told to lie down outside the Turkish bath room on a beach lounger with lots of other loungers. The towel I lay on was wet. A man cleansed my face, then put some cream on it and told me he would be back. After about 20 minutes he came back and then took me to the ladies toilet and washed my face in the bowl. We all decided we would not go back