Minato used the Dead Demon Consuming Seal to seal away the beast's Yin chakra.
It didn't go inside him. He had the Shinigami devour Kurama's Yin chakra so that the weakened Tailed Beast's composition would be purely Yang. That way it could be sealed into Naruto.
My thoughts exactly, Hiruzen sealed Orochimaru's arms, and they returned to him the moment he sliced the belly of the shinigami, the same happened with the 1st and 2nd Hokage, If I had to bet, I'd say the YIN chakra returned back to Kurama, the original owner.
Meaning that Kurama is now 10x its normal size and Naruto's power has doubled.
D'oh >_<; had confused the two, heh arguing semantics pretty much now, but thanks all for pointing the error out~You were informed wrong.
Kurama's chakra was sealed inside the reaper's belly.