Perfect Jinchuurikis has an easy way to get out of Genjutsu but they are not immune to genjutsu.
Immunity is not just the right word.
^ This
When most of the people say: Jinchuriikis are immune to genjutsu, they are just saying that the guys with beasts inside can get rid of genjutsu easily, not "immunity" to genjutsu, although in this case is almost the same: you fall in genjutsu, your beast cancels it, so you basically are exposed to genjutsu the moment the caster cast a genjutsu, no longer than that.