There are a few threads discussing the Hampton Bay Fan remote you can check from the forum search. One of them, Question about Hampton Bay fan and light [Solved], has some good info. The manual on the HD site may also help explain. The remote controls the fan speed and lights (by RF I think) but the control box that goes in the fan canopy also has a Zigbee radio that Hubitat can control. The post also mentions that you need to have a good Zigbee mesh. As @scottgu3 said, you could further control overall power with an existing switch (Lutron or hardwired).