It wasn't sealed inside of Minato. It was sealed unto Minato's very soul, and the two bound pieces, Minato's Soul and Kurama's Yin Chakra were sealed together into the Shinigami's belly. Minato's body died a regular death, but Minato's soul didn't go to the Pure World like it would have naturally. After Orochimaru broke the seal, he bound Minato's soul to the Edo Tensei. However, Minato's soul still had Kurama's Yin Chakra bound to it, so Kurama's chakra was restored inside of Minato's reanimated body. This created a similar effect to a living Jinchuriki. However, Minato later attempted to transfer Yin Kurama to Naruto to save the latter's life. As a result, Minato's soul was unbound from Yin Kurama's chakra and so when Edo Tensei was released, Minato's soul could go to the Pure World as i