Domain mapping conflicts with the Appearance > Customize settings

The Domain Mapping plugin, when activated, and a site has a domain mapped to it ( maps to, clears out the screen for the Appearance > Customize. When clicking the Appearance > Customize section in the Admin page for the site, you get a blank page on the customization screen and you only see the widget on the left.

The bug exist on another domain mapping plugin, and there's a workaround for it. Wonder if we can incorporate the fix to this plugin:

Please let me know if you need any further details.