Ejecting USB drive via AppleScript does not make drive power down
For starters, the greyed-out appearance in Disk Utility means the disk is unmounted, not ejected. An ejected disk does not appear at all. 

The reason it shows up is that when the Cinema Display wakes, the computer sees the drive show up just as if you'd plugged it in. (Honestly, I'm surprised it doesn't mount all the way and show up on the Desktop.)

One thing that can help (particularly in the case of your second script) is to use the internal disk identifier instead of the disk name. You can find the identifier by going into Disk Utility, selecting the disk (or partition) in question, and pressing the Info button (or hit ⌘+I). In that window, look at the label next to "Disk Identifier:". A disk (whole hard drive) would look like "disk0" or "disk2", a partition looks like "disk0s0", "disk0s2", or "disk2s1". Instead of using diskutil eject DriveName, use diskutil eject /dev/disk2s0.