It seems that one eye can be activated at a time. Sasuke has shown the ability to do this, as stated above by Otibo. But it was also done by a Hyuga in chapter 437, page 10, when Hinata jumped into the fight with Pain. She had only one eye activated at the time. So it's possible that Boruto activated one Byakugan at the time--probably a method from the authors to build suspense and make us wonder.
This is all just a possibility, though. He could have very well received the Byakugan through transplantation.
