I don't have an Alexa and can not easily test this. A quick scan of the Alexa modules wiki page though seems to indicate that the Alexa module expects a device to have a "set on" and "set off" command. The Daikin module currently has no such commands, you will need to specify the full "set power on" and "set power off" commands to turn it on and off.
You might get away with a simple EventMap to fix this:
attr <your daikin device> eventMap { usr=>{ 'on'=>'power on', 'off'=>'power off'}}
If not, try the patch that I've attached to add these commands to the module. If that works, please let me know and I'll commit those into the main branch.
The wiki page seems to be a work in progress, as there is no information on what the module expects a thermostat or other HVAC type-device to expose in terms of readings and commands to control the setpoint.
The author of the Alexa module might be in a better position to help on that and give pointers as to what must be done to make this fully compatible. I'd be more than happy to add something to make it work out of the box, but I would appreciate some pointers on what we need to make this compatible.