I'm 99% sure that you need to water. Greatly increasing the humidity around your tree should also be a major concern because even though the leaves are dying, you don't want the buds and the rest of the plant to dry up and eventually die. Humidity will prevent that.
Here's why I think this has happened: It's likely that your plant is young, has an underdeveloped root system and was shocked when you brought it inside. The microclimate (temperature and humidity) immediately changes when moving plants, which can cause younger plants to be shocked. Kind of like when your cold and jump in a warm shower. Even if watered properly, underdeveloped root systems don't bring up enough water, which causes the plant to dry out and eventually die. Be careful of dry air being blown onto your fig, which is causing it to dry out.