If you use an evaporator tower you do need to replenish that water. The tower is usually used to cool a closed loop of water (or glycol/water mix depending on the climate) that cools the refrigerant in a chiller.

The system in the article uses a pipe loop underground in place of an evaporator. This uses less water/energy but require a higher first cost and very specific location requirements which is why the cooling towers are still more popular.