Sadly i couldn't figure out what i was supposed to do :(
Viewing post in Rubix Echo jam comments
Definitely a mistake on my part for lack of explanation because of time management (at least the dragon got it...).
You need to just progress through the rooms, however you'll find your way blocked by the gates that need to be activated with the switches. And the switches reset if you keep the dragon outside the rooms in which it was active i.e. the dragon is outside the time loop.