I have louvre window open but moisture laden air is heavier. If it's windy, naturally it will blow inwards or sideways. Chances are, there's an equilbrium. For shared bathrooms, opening the two doors and leaving the fan on in the two rooms somewhat helps but that only transfers excess moisture inwards. Hence for a bathroom, the extractor fan does the job much better.

Just updating that in the UK, this type of switches are also called time lag switch

is there any switch with capacitor function which left the ventilator fan continue to work for 5 min even after we off the switch?