As long as you are signed into the Mac with the same iCloud account used on the iPhone, this will download them all. No, you do not need to get them all downloaded to the iPhone ever for any reason for this to work. Period. You need to stop repeating that, because it is wrong. How many people have to say the same thing?
Yes, you will have to go into a hidden folder to access the Originals once they're downloaded if you want to copy them somewhere else, but it's like two clicks.