Hosts that are not in perfect partnership with their bijuu don't have the added benefit of being able to negate most genjutsu, it isn't about taking control of the chakra from the bijuu. Naruto when he had just KM would not get the added defense against genjutsu. Just wanted to put that out there before I explained something.
Genjutsu can be broken by a few ways:
Physical pain not caused by the genjutsu.
Disrupting your chakra.
Having someone else disrupt your chakra
(added caveat - People with doujutsu, with their ability to see chakra, are able to tell if other people are in genjutsu, and are able to see through genjutsu easier. Being able to tell that you are in a genjutsu does not equate to being able to break the genjutsu though)
Anyway so a perfect host can have their bijuu disrupt their chakra for them to break them out of genjutsu but first they must notice it.
Itachi's Tsukuyomi is an obvious exception to this rule as it takes place instantly, not letting anything happen in real time, so no chakra disruption will take place.
Also I would like to point out that this does not mean that they are always immune to genjutsu. Yagura (the 4th Mizukage, who was also a perfect jinchurikki, was under a genjutsu by either Madara or Tobi. )
