Clearly not extinct. They were hibernating, waiting for the signal. Dragons were mentioned for a long time in history, and science. Many had tried to disprove their existance because of their disapperance, but the random writings about them in different cultures stated otherwise.
Besides, when was the last time you actually heard about a phoenix? Dragons were still complained about during medieval times. The last time I heard about a phoenix of any type was when a peacock was mistaken for one.
What would you like me to do, pull a giant flaming bird out of my top hat that a carry around? I'm not the magician.