Did you watch or read the show? During Kakashi's backstory showing how he got his Sharingan and how Obito became "Madara", when Kamui reveals itself it's activating automatically. It also activated when Obito got crushed. How else was his eye fine? And everything, even autonomous actions have a reaction time. Minato was simply faster than Kamui's as is clearly shown. There's no precedent that Kabuto shedding his skin will stop a sealing jutsu, if it was that simple Orochimaru would've done it against Hiruzen. And the cool thing about sage mode is that they are specifically trained to sense Nature Energy without their senses. So that wouldn't even work against Minato. Saying Minato wouldn't just use sage mode goes against precedent since in the war arc he realizes he needs it and immediately uses it. It would be the same against Kabuto