There is a controller option you can pass to hyper-spec mount but it doesn't seem to work properly. The default hyper-spec controller doesn't inherit from your app's ApplicationController so you won't have access to any custom methods, Devise current_user or Hyperloop acting_user. Basically unless you're testing a very simple public component the default test controller setup won't work for you.
The workaround for now is to pre-define ReactTesrtController somewhere and make it inherit from your ApplicationController:
class ::ReactTestController < ApplicationController
end