It must be something like that, but I cannot get it to work...
When I open the PDF on the Android device, I see the updated PDF.
When I open the PDF from the Windows desktop via USB, I see the empty PDF. The same if I drag-and-drop it to the desktop's Documents folder.
I disconnected the USB cable, and I even restarted Windows, but I cannot get the updated PDF.
But ... I just made a little experiment: I connected the Android to a different Windows desktop, and here I can see the updated PDF on the Android device!
So you are absolutely right with your assumption; I am getting an old, cached version somewhere. But this, at the end, has nothing to do with Adobe Reader; it works as it should.
Nevertheless, if you have some additional advice for this Android newbee, I'd be grateful!