You should distinguish between "ethereal" and "incorporeal." It is confusing at times, but they are two different things.
Incorporeal simply means having no physical body.
Ethereal means existing on the ethereal plane.
Though there are instances of overlap, they are usually two distinct things.
Incorporeal creatures are not necessarily ethereal, in fact most incorporeal creatures exist solely on the material plane when they are on the material plane. Shadows, Wraiths, Allips, and in PF Ghosts are all incorporeal creatures that are not ethereal.
An ethereal creature exists on the ethereal plane and not on the material plane. Just because a creature is on the ethereal plane does not mean it is incorporeal on the material plane, usually it simply does not exist on the material plane at the same time. Phase Spiders and Xill are creatures that can bounce between the two planes with ease, but are not incorporeal.
(In 3.5, ghosts were a bit problematic because they were both ethereal and, when manifested, incorporeal. This often led to the confusion between ethereal and incorporeal.)
The Blink spell is special in that it causes the subject to be incorporeal and invisible to the plane that hes not on at the moment.
Spectral Hand has nothing to do with etherealness. It simply has no physical body and is thus incorporeal. A spectral hand cannot reach into the ethereal plane on its own. Nor does it get any benefit against incorporeal targets (just as incorporeal creatures gain no benefit against other incorporeal creatures).
All that being said, what you've described is right. The spectral hand goes with the mage to the ethereal plane when blinking, so there is a 20% chance that the mage and the spectral hand are on the opposite plane from the target.
Note also that Ghost Touch weapons only benefit against incorporeal creatures. Using a Ghost Touch weapon would not allow the wielder to attack a Phase Spider that just jaunted to the ethereal plane.