Board Thread:Theories and Speculation/@comment-30355627-20170128224827/@comment-1751565-20170129163838

Kurama's sensory is hostility. Minato's own sensory is chakra sensing, same as Tobirama. As sensors of Chakra, Tobirama is more powerful than Minato in that aspect, thus his reflexes to dodge and act are quicker.

After all, the Fox at one point in time, even told Minato to "change his chakra to sensory mode" so that he could detect Gaara and Sakura incoming with a 'near-dead Naruto'. Because Minato clearly did not sense them before that, when he was busy fighting Black Zetsu with Kakashi.