I gave you the kabuto example where he's not making physical eye contact, yet it would still affect him.
Sure Nagato heard the song, Nagato hears what his bodies hear. He most likely saw what the bodies saw in the illusion. He knows genjutsu doesn't last forever, he could've just waited until the genjutsu was dispelled before he summoned the other bodies. Which is what he did. He didn't summon the bodies when his other bodies were in a pinch. He waited until the genjutsu was dispelled.
The thing about the sharingan mangekyou is that it really is hypnotism, when people look into its eyes
The translation of tsukiyomi from the Databook:
Tsukuyomi description: (this is the bottom right)
Within the Sharingan's telepathic and hypnotical powers, the greatest genjutsu was created out of hypnosis: Tsukuyomi. On this earth, people are subject to things like time, gravity and air, and the people who can maximize their abilities are the ones who decide who is the winner and loser. However, Tsukuyomi gives the user the ability to drag his opponent to an imaginary world that the user builds, and restricts him in it.
Common sense does not apply in this imaginary world like it does in the real world. There is no possibilty of dispelling this genjutsu. People caught in this genjutsu do not know when this imaginary world will end, and the user controls everything. He shows them the punishment of hell. It makes the person caught in it crazy. Even if you are strong enough to break rocks, or fast as lightning, it matters not before this technique....that's why this technique is feared.
(Top Left)
The owner of the title of"The Greatest Clan" the Uchiha clan's bloodline limit Sharingan. Within them only those at the top level with the "Mangekyo Sharingan" can use this technique. At the same time, only those with Sharingan can dispell Tsukuyomi... only special level shinobis can use this. Only those blood relatives of the Uchiha clan who are blessed with talent can recieve this heavenly technique"