How can I treat these green spots on my hot tub?
The green stuff appears to be algae. It is most likely growing there because that area gets wet occasionally with the treated pool water but then is left exposed to the air without the water present. 

The way to control that on most hot tubs attached to a pool would be to normally set the water diverter valves at the pool pump to circulate the pool water through the hot tub and then to the pool. Pools that I've had experience with will still permit some of the daily pool pump circulation to go to jets in the pool proper. If you keep the chemical balance in the pool correct the flow of treated water should control algae growth. (BTW I think only testing and adjusting your pool chemical state every three weeks is far too long of interval. This should be done every week so you can stay on top of things when climate conditions change). 

With persistent growth like showing in your picture you may be faced with having to do a direct cleaning of that area after applying some algaecide. The chemicals may require selection as some types are designed for specific colors of algae (yellow, black, green, brown etc).