I RP that all my characters were in Cyrodiil at the time of their arrest, it makes sense as Ralof tells you that you were trying to cross the border, and the carriage is leading away from the Cyrodiil border. However Ralof and Ulfric were captured at Darkwater crossing (think thats what its called) so that could be the 'border' they're referring to
To quote the Book of the Dragonborn: "Very few realize that being Dragonborn is not a simple matter of heredity - being the blessing of Akatosh Himself, it is beyond our understanding exactly how and why it is bestowed." In other words, simply because the Septim Dynasty was Dragonborn doesn't mean that the Last Dragonborn is Imperial. Even if he/she was from Cyordiil, this doesn't prove Imperial ancestry. Considering its proximity to the border with Skyrim, it's more likely that he came from Bruma and its majority Nordic population.