You are actually wrong one this... I would believe that the reason the 4th Mizukage was not able to break out of the Genjutsu is because Obito/Madara not only placed a Genjutsu on the Mizukage but also on his Tailed Beast. The same way Madara was able to place Kurama under a Genjutsu and then force him to fight against Hashirama.
Now it isnt quite apparent how this is done but Sasukes struggle with Naruto shows that at the very least some kind of physical connection with the Jinchuriki is required in order to enter the inner world where the Tailed Beast resides. Once there it can be placed under a Genjutsu much like Kurama, and then subsequently the Jinchuriki could be placed under a Genjutsu as well. - Cause at that point kurama didn't have a jin.
But another thing I want to express about that situation is that what Obito did to the Mizukage goes far beyond regular Genjutsu, he was able to control the Mizukages actions for a very long period of time (I believe a few years). This is pushing it even for a genjutsu. But one thing we do know is that Obito/Madara and Shishui were in contact with each other, evidenced by the fact that Shishui introduced Itachi to Obito/Madara. So it is likely to say that Shishui may have placed the Mizukage under his ultimate Genjutsu, giving him the order to obey Obito. Which would explain the unnaturally long period of time that the genjutsu lasted for.
But either way you are very wrong, yet at the same time somewhat correct.
- Genjutsu is formed by implanting your chakra in your enemy and controlling the flow of chakra to their brain.
- Genjutsu can then be broken by distrupting your own chakra, thus distrupting the enemies chakra within you, and breaking the effects of the genjutsu.
- This genjutsu breaking technique can be done by oneself or by a 3rd party, but it requires extensive chakra control and training to be able to do it to ones self.
- If your a jinchuriki this problem is solved because the tailed beast within you can always perform it for you.
- Thus to bypass this you must incapacitate the Tailed Beast before attempting the Genjutsu, or merely place it under a Genjutsu before placing the Jinchuriki under the Genjutsu.
If I had to guess on how it happened I would say Obito fought the Mizukage, he turned into TBM, and Obito cast the Genjutsu then, which would either place both under the genjutsu since in TBM both the Jin and the TB are in control, or at the very least it would place the TB under the genjutsu,.
