Genjutsu doesn't work on a perfect jinjuchuriki no matter the genjutsu it won't work. and a jinchurik like naruto won't fall for that and never gives up so even if he was not a perfect jin tsykyomi couldn't break him down for gud the guy doesn't learn how to give up sometimes. In two seconds the beast will break the genjutsu and the beast can't get affected by it while their jin affected by the tsykiyomi tsykyomi one of them.
