Now forgive me if this has been answered, and forgive me that I know very little on the subject, as I am a PS3 user and the Dragonborn (DLC) pages are not quite done and many lore pages have not incorporated information acquired from it.

In the DLC Miraak is supposedly the first Dragonborn, but up until now we have known St Alessia as the first Dragonborn. What is going on here?

It seems very open-ended. Miraak supposedly gained the knowledge of using the Thu'um, Bend Will, from Hermaeus Mora, while Alessia got the divine blood from Akatosh. It seems Miraak did not have any dragon blood (if he did, where the hell did he get it and why is the only thing mentioned the fact that he gained knowledge of the Thu'um and used it against the dragons?) and that Alessia did not possess the power of the Thu'um. 

I looked into it, and Miraak was alive long before Alessia. Miraak obviously lived in the Merethic Era, in the days of the Dragon Cult. While Alessia was alive during the First Era. This means Miraak came before Alessia. But was Alessai not perhaps the first to possess the dragon blood?

~Jack Pistol