When bee trained naruto to use the tailed beast bomb, he said to make it you need to put black(yin) and white(yang) chakra together in a certain ratio(8:1 i think) to create it. So yea the kyuubi must have both yin and yang, since he obviously use tbb's. Oh and minato never himself said he sealed the yin half in himself and the yang in naruto. In the flashback chapters minato just says he will seal half of the kyuubis chakra in himself and the other half in naruto. Jiraiya is the one who said minato sealed sealed the yin chakra into himself and the yang into naruto. He said this right before he fought pain, when he released the toad with the key for narutos seal.How jiraiya knows this since minato died right after sealing the kyuubi i don't know, that's why im inclined to believe minato himself instead.
So basically narutos kyuubi still only has half of its total chakra, and minatos gift should be the other half of kuramas chakra, making kurama be at full power again.