You know how his intangibility works right?
If Obito still want to have a view on battlefield, he will not send his eyes part/head into Kamui.
You must be registered for see images
Look at the scan.
He sent parts of his body into Kamui completely but still maintained his eyes and half of his head inside reality world. Thats mean for Itachi what he need just lunch the Genjutsu(Tsukuyomi) on Obito as Obito still have his head/eyes inside Reality world and vulnerable to Genjutsu.
Yes 80% of his body parts were inside Kamui dimension but not his eyes/vision in which Genjutsu's chakra can be transfer through it and effecting whole Obito's body unless he send his head inside Kamui land also.
And not because Genjutsu will pass through Kamui land but Obito cut the link from outside world.
Plus his awareness on Genjutsu activating near zero bcus he was not a best sensor.