I've the updated version of Adobe Draw on my iPad Pro and Illustrator on my MacBook Pro. If I tap the drop-down-menu in Draw to send my file over, there is a loading icon until a small window pops up: 'sent!' But nothing happens on my MacBook in Illustrator. Also there is no way that I have two different accounts connected. What else could it be?
Problem solved. The Creativ Cloud App on my Macbook seem to failed. A restart helped, after that all documents opened automatically in Illustrator CC.