I don't see that it matters much which way the fan is blowing. What matters is the air exchange, which is about creating an airflow.
If you have a multistory house you can open windows at the top and bottom, the warm air will tend to flow out and pull cool air in the bottom. In that situation if you have a fan, it would make sense to have it blowing air in on the lower level, or out on the upper level.
If you have a single level, the fan will just create a slight pressure difference in one direction or the other. You just need to open several windows, preferably on opposite sides of the room, and if you use a fan to pull cool air in that creates a positive pressure inside the room, which will force the warm air to be exhausted through the other open windows. If the fan is blowing warm air out, then the room pressure will be negative relative to the outside, and cool air will be pulled in through the other open windows.
If you have a multistory house you can open windows at the top and bottom, the warm air will tend to flow out and pull cool air in the bottom. In that situation if you have a fan, it would make sense to have it blowing air in on the lower level, or out on the upper level.
If you have a single level, the fan will just create a slight pressure difference in one direction or the other. You just need to open several windows, preferably on opposite sides of the room, and if you use a fan to pull cool air in that creates a positive pressure inside the room, which will force the warm air to be exhausted through the other open windows. If the fan is blowing warm air out, then the room pressure will be negative relative to the outside, and cool air will be pulled in through the other open windows.