The answer to the question of whether you need to open windows for evaporative cooling is both yes and no. While it’s true that in order for evaporative cooling to be effective, outside air needs to be drawn into the house through an open window, opening a window isn't always necessary. If your home has a fan or blower (such as those used with central air conditioning systems) then this can provide all the airflow needed for evaporative cooling without having to open any windows. Additionally, many modern homes are equipped with mechanical ventilation systems which will provide enough airflow on their own while also providing fresh air exchange throughout the entire house - again, eliminating the need for extra ventilation via opened windows.
For maximum effectiveness when using an evaporative cooler it's important not only that there's adequate airflow but also that you're able to achieve cross-ventilation - meaning you have one window opened at one end of the room and another at the other end so that cool outside air is pulled into one side and warm indoor air is expelled out from another side. In some cases this type of setup won't work due to physical limitations such as furniture placement so if this is something you struggle with then simply opening up multiple different windows throughout your home can still help circulate cool outdoor air more evenly around your living space - even if it isn't necessarily optimal cross-ventilation conditions.