Documents/My Kindle Content -- sounds suspiciously like your Mac user account's Documents folder, and specifically the subfolder containing your Kindle for Mac books.
Are you absolutely sure you are putting the files into the mounted drive? It should have a label in the bookmarks panel in Finder.
And an eject icon, because it is a mounted drive.
FWIW -- Not being a Mac user either, I am nevertheless 99% positive Macs put externally mounted drives in the /Volumes folder.
ETA: And yeah, like knc1 said, it should have "documents" and "system" folders in there already. "{kindle_drive}/documents" contains your books. So that would be another giveaway...