I don't think Drasna is from Sinnoh but her Grandparents are.
Pokémon X and Y
Before battle (rematch)
"Oh goodness, hello to you! You know, my grandparents came to Kalos from a distant region. They came from a town where the past lives on... When I was growing up at their knees, they raised me on tales of the Pokémon of time and space. It's really thanks to those stories that I decided to become a Dragon type Trainer."
It sounds as though her grandparents came to Kalos from Sinnoh and settled down there.
>In Pokémon X and Y, Drasna appears as an Elite Four Trainer of Kalos. Her grandparents are from Sinnoh and taught her about the region's mythology surrounding Dialga and Palkia, which inspired her to train Dragon-type Pokémon. Drasna also has a relaxed composure, which hints at her strength that knows no bounds.