Recently I came across an instance where I was covering for a colleague (she did not have any pending approvals out so she did not designate her approvals to me) and I had to send a document approval to her client. She returned before the approval was sent from the client and I never received a notification of the approval, yet I was the one who set it.
I called customer support and found that if the Project Ownership had changed back to my colleague before the approval was sent and if I was not the Document Owner (I was not, our designers upload the files, we review and then if no errors we assign to the client for approvals), then the expected behavior is that I would not be notified of the approval.
This is odd to me, as I feel whoever sets the approval should be notified. Design does not care about approvals (in our case) and if the approval came in during the night time and transition from me covering my colleague vs. not this could have definitely gone unnoticed and caused a delay in the project. I am not sure what the "right" solution is here but how the behavior is today is definitely not intuitive. Happy to collaborate further on this one - thanks!