The exception proves the rule. Obito also controlled a perfect Jinchuriki. Normally, Bijuu free their host from a Genjutsu after realizing it like an ordinary partner. The Jinchuriki gets caught in a Genjutsu and experiences its effect, until his Bijuu disturbs his Chakra flow and frees him.
Tsukuyomi is such an exception. Bee is right, when he says that, in order to break a Genjutsu, you need a partner who distrubs your Chakra flow and snaps you out of it, which in this case is his Bijuu. But, the exception of Tsukuyomi was stated in the Manga:
You must be registered for see images
Genjutsu do affect Jinchuriki, their Bijuu just snap them out. As Tsukuyomi is, as stated by Kakashi, is instant, partner tactics won't work. Naruto also warned Bee from Tsukuyomi, despite he is a Jinchuriki.