No you don't, Rails takes care of reloading your code automatically. But this code reloading support is limited. For example changes to application.rb are not applied until you restart the app server.
But I would recommend Phusion Passenger over Puma. Phusion Passenger is a lot easier to setup, especially when you hit production. Phusion Passenger integrates into Apache and Nginx directly and provides advanced features like dynamic worker management. Phusion Passenger is very mature, stable and performant and used by the likes of New York Times, Symantec, AirBnB, etc.