De acordo com Wookiepedia, Vader segurou uma postagem oficial do Imperial: Supremo Comandante das Forças Imperiais .
No entanto, como você nota, ele foi por um tempo subordinado ao Grand Moff Tarkin. De Wookiepedia:
During the Battle of Yavin, Lord Vader was apparently only Palpatine's observer aboard the Death Star, with operational control in the hands of Grand Moff Wilhuff Tarkin, who was clearly capable of "holding Vader's leash"; soon after, however, he was given command of the forces charged with prosecuting the war against the Rebel Alliance, and perhaps a wider commission to maintain order throughout Imperial space. His new powers may be presumed to have been conferred by the time he returned to destroy the Rebel base: by this point he had taken charge of Executor, the largest warship in the galaxy, as his command ship; and Admiral Griff and the Sector Group of the Bright Jewel Oversector—one of the most important Navy commands in the Empire—were subordinated to his command.
(em negrito, seções principais)