Diagnosis
This is a wiring or configuration issue. The ecobee needs to know you have a furnace (where the fan is controlled automatically by the furnace itself) vs. a boiler with separate fan control. The 'G' wire must be connected.
How to Fix It
First, check your wiring at the thermostat. You must have a wire in the 'G' terminal for fan control. If it's there, go to Settings > Installation Settings > Equipment > Furnace. Go to the 'Fan Control in Heat Mode' setting. It should be set to 'Furnace' (meaning the furnace controls the fan), NOT 'Thermostat'.
If That Didn't Work
If you don't have a 'G' wire, the ecobee cannot control the fan independently. Your old thermostat might have been jumpered. You'd need to run a new wire or use the PEK to free up a wire to act as 'G', which is a more complex rewiring job at the furnace.
Heads Up
If you have a heat pump, the settings are different. For a heat pump, you need to ensure the 'O/B' reversing valve is configured correctly in the Equipment menu, or it can block fan operation.