That fan comes with a remote control canopy module. It expects 120v so that is why you cannot use a solid-state fan control. Now this said if you have 14-3 Romex (2 load wires 1 for light and 1 for fan) then you can skip the install of the canopy module and use the GE switches you mentioned in the original post.
If you only have 1 load wire running to the fan, search this forum because Home Depot now sells a Hampton bay fan module/remote that can be integrated to ST via custom device handler from @dalec