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1. first, Kyuubi switches with Naruto. Thus, Naruto is not controlling his body anymore. Rather, Kyuubi is in control.
2. Second, Kyuubi connects himself to the chakra circulatory system of Naruto. This means he is feeding his chakra into the system.
3. Then, he gave that chakra to Kakashi.
Thus, the system Kyuubi used is the same as the one Naruto used later. In fact, Kyuubi planned initially to teach it to Naruto. His only problem is that Naruto learn quicker by feeling things instead of learning the theory. Consequently, before Kyuubi explained the techs, Naruto had already figure it out. Even in that chapter, Naruto said that he has started to figure out how things work.
Clearly, there is no contradiction. Moreover, I still don't understand why the fans do not see the fact that the first Shinobi got his knowledge from taking Shinju power, and the person who created ninjutsu was born with the same power (Shinju's power). This tells us that at some point, a jinchuriki will become the most powerful shinobi.
Madara explained that Hashirama's chakra was from Shinju and we saw evidence when the tree absorbed chakra. This also said that even Sharingan is the result of Shinju's power.