This is normal for your tree to break dormancy prior to the weather warming enough to place outside. The Fig has an internal clock that tells it to start waking up.
Keep the Fig in the cool location, check the soil and began to increase watering--lightly. You can place the plant in a location that has more light, but not direct sunlight.
You still cannot place the Fig Tree outdoors until danger of frost has passed. The new leaves are very sensitive to cold.
https://www.gardeningknowhow.com/edible/fruits/figs/fig-cold-protection.htm