Sorry for the confusion here. Please don't use Appearance -> Customize options. Instead, use X -> Theme Options -> Typography area for X theme specific customizations.
For example when you head over to Dashboard -> X -> Theme Options area, you can click on the settings icon on the bottom left hand corner.
Then you can access font manager from there and set a font according to your requirement.
For example you can add a new font as below.
Then when you're editing your content through Cornerstone editor, you can access to those fonts.
Hope that helps.