Is Minato a Jinchuuriki? I wonder why Minato is categorized as a Jinchuuriki, considering the following:


Madara couldn't be Ten-Tails' host because he's re-animated, and he has to force Obito to revive him
Minato is re-animated, just like Madara, and yet he has half the Kurama inside


It's possible that he sealed in him half of Kurama before he died, and yet why on earth Kurama wasn't reincarnated
Or Kurama was sealed in unusual manner that Minato's case defied the norm on sealing tailed beast
Let's make things straight:


The former Jinchuuriki, reanimated and reinfused with their respective Bijuu, had the Yin-element rod channel the chakra back from the Gedo Mazo. Once removed, Tobi had to quickly re-seal them inside of the statue, or risk them being freed.

The seal wasn't a permanent seal, like Naruto's or Killer Bee's, it was a temporary seal used for battling and then removing easily.
Minato's case is a bit different. Minato used the Shiki Fuujin to seal Kurama's Yin half inside of himself, but then, he himself got sealed, along with Kurama's half, into the Death God. That's why the Yin half of Kurama never revived (As it was still sealed), and that's why when Minato got reanimated with Edo Tensei, Kurama was already part of the deal. 
Madara, however, cannot be a Jinchuuriki because when he died, he wasn't. The Edo Tensei revives people at certain states of their lives (usually the time of their deaths, but not always), Madara was not a Jinchuuriki anytime in his life.