A discussion was started regarding the visibility of whispered posts in Discourse. not-ethan pointed out that hovering over the eye icon on a whispered post displays a message saying it’s only visible to moderators, even if non-staff groups have been given access to whispers. However, Joseph_Hansen disputed this, claiming that whispered posts are not visible to non-moderators. The issue was acknowledged by JammyDodger, who explained that the description hadn’t been updated after the introduction of “whispers allowed groups”. A fix was later committed by jancernik, updating the whisper tooltip to reflect the configured “whispers allowed groups” value.
In a whisper, you can hover over the eye icon 
and it will say:
this post is a private whisper only visible to moderators
Even if people are not and are visible to other non-staff users.
Repro:
This isn’t true, at least not in my experience- whispered posts aren’t visible, even as a “hidden reply”, to users without access. I just tested it to make sure; a topic with one whispered reply shows no replies (it doesn’t even show the infobox that gets added with replies) to a non-moderator
You can now use whispers allowed groups to make them available to more than just staff users, but @not-ethan has found a description that hasn’t been updated to match yet. 
This commit should fix this. Now, the whisper tooltip is dynamically filled with the value of whispers allowed groups (if configured).
https://github.com/discourse/discourse/commit/d633467c6086b7aaec380b17dd5cab8b02263b86