First option: She does have the dragon's blood within her from her ancestor, either some kind of illegitimate child who was banished or a fallen noble family. Either way, being hit with the Emperor's magic triggered her dragon blood and awaken her magic.

Second option: She has a special constitution where she absorb the an instance of magic she encounter and her body become able to use that magic either temporarily or permanently afterward.
i.e. she was 'colorless', and he just made her into his color (and also make her magic have 'perfect compatibility' with him ;) )

Third option: The brown/ginger hair was actually dyed to avoid trouble of having a golden hair (symbol of the royal family), and the Emperor's magic removed it.