Some mysteries, namely interruption/control ones, will always take priority, regardless of where your ninja is placed. What is your p4 ninja?

It seems that Kakashi will always go before Minato on auto, I know a person who had the exact same problem and he weren't able to solve it. You could try lifting up your ninjas and/or removing everyone from lineup and placing them in order [first - J. Minato, second - x, third - S. Kakashi] or the opposite order, although I doubt it'll work.