For anyone who has this problem, I managed to find a fix. It required modifying the plugin. But essentially, you need to open up the jquery.lightbox.js file in the plugin, go to line 192 and add:
caption = jqThis.parent().find('.tiled-gallery-caption').html();
The plugin by default doesn't look for the tiled gallery captions since the classes are a little different. Additionally, you'll either need to covert this js to a jquery.lighbox.min.js and overwrite the original or go into wp-jquery-lightbox.php and change line 22 to define jquery.lightbox.js
Hope this helps anyone else who might come across the same issue. Perhaps this can be added to the next release of this plugin!