I notice if I use a solid color background (for example, pink) in place of the background image, then
the corners are colored in with the color specified, but not if I use a background image repeated to
cover the full page.
Sounds like the plugin is smart enough to detect the background color the corners are sitting on top of, but it can’t figure that out if it’s sitting on top of an image that is using a different color. I’d say just make sure you use a flat color and make sure to set the background color of the page element directly beneath the element getting rounded corners to match.