A custom theme CSS file should be a modified version of the original 'web/jbcore/theme.css' file, pointed towards within the gallery's embedding code using the themeUrl configuration option (as documented in the Theming Guide).

If a themeUrl is used, then Juicebox will use the CSS file that the themeUrl points towards, instead of the original 'theme.css' file (which will not be read or used at all.)

Try setting up a test gallery with a themeUrl which points towards a blank CSS file.
The gallery will not be displayed at all, indicating that the original 'theme.css' file is not being loaded in the web page.

According to the 'Inspect Element (Q) -> Style Editor' list in Firefox 23.0.1, the 'jbcore/classic/theme.css' file is not being loaded on your web page (only the 'jbcore/delosgaia/theme.css' file).

Likewise with 'F12 -> Resources -> Stylesheets' in Chrome 29.
The 'jbcore/delosgaia/theme.css' file is listed but the 'jbcore/classic/theme.css' file is not.

Can you provide some steps that I can reproduce to find out where you are seeing that the 'jbcore/classic/theme.css' file is being loaded?

If the 'jbcore/classic/theme.css' file is being loaded in your web page (though it should not be and my checks above seem to confirm this) and it is somehow conflicting with your modified theme, then a quick fix might be to simply delete the file.
Otherwise, if you need to use the original 'jbcore/classic/theme.css' file in other Juicebox galleries in other web pages, then try renaming the file and point to it using a themeUrl in the galleries which require it. In doing so, the Juicebox gallery on the page you quoted will no longer be able to load the original 'theme.css' file (as there will be nothing in the default themeUrl path and the gallery will not know of any themeUrl used in other galleries in other web pages).