I did a complete new installation of WordPress using the Twenty Thriteen theme.
Added a feature to the sample page. The went to Media Library, selected the image, cropped it, saving crop to apply to thumbnail. Updated image.
The thumbnail in the media library changed.
But the appearance of the feature image on the page does not.
I tried again this time cropping the image to apply to all image sizes.
Still no change.
Then went to sample page and deleted featured image and added it back again.
Still no change
Tried on several browsers and refreshing cache.
Does Edit Image work on featured images? If so can you tell me the exact steps you did that make it work?
Here is the test page: