He was brought to the present by his father before Yuya, using his knowledge to create the Leo Corporation while making preparations to capture Yuya, whom he refers to as the "Destiny Factor" that will eventually chose to destroy the world.
He was brought to the present by EVE's group months before Yuya arrived, using his knowledge to create the Leo Corporation. Reiji proceeds to set up a group of Duelists and other preparations to capture Yuya, whom he refers to as the "Destiny Factor" that will eventually chose to destroy the world.