The problem is you're confusing the different cloud services.
iCloud is an Apple creation and only works for Apple applications or a handful of Mac OS X apps that have managed to implement its programming hooks. It is NOT recognized by any Adobe product.
Adobe has two cloud products: The one which works with Adobe Reader is Acrobat.com. You can upload and download files if you have an Acrobat.com account.
Adobe also has an Adobe Creative Cloud service which also has nothing to do with Adobe Reader.
This document describes how to move PDFs into Reader to view them (but doesn't describe Acrobat.com):
This document describes how Adobe Reader works with Acrobat.com: