I was taught that the "neck" hand should rest pretty much at the top of the spine, with the spine lying in the "V" between the fingers and thumb. From there, the feeling is more of the hand falling toward your own center, NOT pushing/pulling uke downward.
Exactly what this does to uke's body will depend on him. A more flexible and responsive person will lower their center to try to keep their alignment, allowing you to "bounce" them back up and leading to the "classic" irimi nage back fall. A less responsive person is likely to bend at the waist, leading to either a faceplant or a forward roll.
Interesting...I was originally taught that the neck hand should be on the side of the neck, so the fingers could dig into the nerve cluster behind the jaw on an uncompliant uke. And that uke's head should be brough to about your shoulder, or at least towards if they don't bend all the way. All seems fine on paper, but I've never been very good at it.