Possible dumb question, but is Daenerys responsible for magic?

I’m rewatching the show so apologies if this is just a D&D fabrication and not book lore. But until Daenerys goes into the fire and hatches the dragon there seems to be no magic in the world (aside from the walkers). Stannis’ shadow, Dondarion’s resurrections, the leeches, etc. all come after the hatching.

It wasn’t until she was in Qarth, when she meets the warlock and he says something like “your dragons returned our magic to us.”

Is that accurate? That her dragons allowed magic back into the world? Or am I reading too much into things?