I played someone who got banned. Our play is still on, with my opponent to play "a few minutes left" for about two weeks. What will happen?

some thing is wrong ask the staff

I have enabled "Automatically win on time" now and the game is declared a win for me: thank you for your advice!

Because some don't want their game to end on time or they'd rather wait for their opponent to move than have a win on time.

Makes sense, really, if it were the other way around the decision would be automatically made for you when the situation first arose.  This way you can determine how you want the game (and any future games) to end when you have an opponent time-out.