Frustratingly vague. I was unable to reproduce when the original article was posted. I did not test exhaustively, but I was able to get HME to reject messages in various ways (mostly by sending oversize messages) and none disclosed my real address because they were rejected before any rewriting to the final address occurred. And in looking at messages that were delivered, I didn't see any additional SMTP servers in the path that would reject the message.
The most I was able to leak was a DMARC header showing my real domain, but even that only occurred when I replied to an HME email from my real (non-icloud.com) domain. When I updated HME to use my icloud.com address, even that leak went away (but it did make it clear that HME was not sanitizing message headers).
Maybe if you have HME setup to forward to a non-icloud.com domain and that domain's SMTP servers rejected the message as spam, I can see how this could occur. But if forwarding to an icloud.com address, no way this should've been able to happen in the first place.
I wish they'd included a sample message including full headers to see the vulnerability in action. Where in the delivery path was the bounce being generated?
I want more details.