I have an EditorTools.xml file set to include an ApplyClass tool. In the cssFiles section I have an item with name="~/styles/editorstyles.css". This css file has the classes I want to be shown in the Apply Class dropdown. This works in Chrome, but Firefox does not show the classes in the dropdown. I used the Network monitor in the Firefox developer tools to verify that the editorstyles.css is being requested and downloaded successfully.
Using Firefox version 32.0.3 on OS X Mavericks 10.9.5