it's all about the class.
if you look at the code that wraps around your gallery, it should have a class, i.e, ".content, .entry, .something, etc." Since this is about putting multiple galleries on one page, you would need to specify the class further so that fancybox can distiguish between different galleries.
.ngg-galleryoverview worked for me and should work for you. the issue is where do you specify it. Like i said, the easy fancy box plugin made this easy for me. i enabled an option, then added the class to a list, and presto! Fixed.
Since the assumption is that you guys are using a different plugin, I don't know where you would put it. if you tell me the exact name of the plugin, i can look at it and maybe hep out.
but fyi, easy fancybox uses fancybox js itself, it just adds an extra layer to make, well, easy!