You seem to be under the impression that there shall be no condensation.
You would need a wind tunnel for that.
There is the point that if that is what happens in your bathroom, that is no condensation whatsoever with the fan on, then perhaps you don't need the fan at all.Strange conclusion .?
It will do no harm for the tiles and mirror to mist over (it shouldn't get to running down) while you bathe, (you will notice there is no condensation on the towel, Why is that? Because a towel absorbs moisture, surely you would know that) then when you finish, either open the window or leave the door open.Good way to transfer damp air to the rest of your property, hardly to be recommended .
If the condenstaion is not gone in ten or fifteen minutes then you have, as I said, more fundamental problems.