If you've recently made big, splashy changes on your site you're probably itching to see how new users are enjoying your hard work.
If for some strange reason the new sessions you're recording in FullStory seem to show your old website, you may want to check how you're serving your new CSS files, as well as the expiration date on your old CSS file headers. If the expiration is set in the future, your site visitors may have to refresh the page in their browser to ensure they're seeing your new design. With respect to adjusting how resources are served, you may want to see what Google has to say here.
FullStory's resource cache will continue to use the old copies we've stored until our cache is refreshed, approximately every 6 hours. This means you may see the old site version in your new sessions until the cache clears.