Information from the novel.
Essentially Jaryuu is a genuine harmless herbivore dragon. The image of evil Jaryuu people think of him thanks for some funny misunderstandings is the source of Reiko power. In that world, image = magic. For hundreds of years his false image as a fearsome powerful dragon manifest into a real magic power just like how people thought of him.
Originally it should be Jaryuu power, but because he didn't acknowledge the existence of evil and powerful Jaryuu people think of him, the power is no one's. It just floats in the air, until Reiko acknowledged herself as evil Jaryuu's kin. So the power move to her rather than to the dragon.