I use Mark Jaquith's solution (see here) to stop my stylesheets being cached. Not sure it applies in your case, given it happens on a new browser, but it's worth a try.
In essence you append the file modification timestamp to the URL, so when the file changes, the browser thinks the URL has changed and downloads the latest version. Mark's example, for the theme stylesheet:
<link rel="stylesheet" href="<?php bloginfo('stylesheet_url'); echo '?' . filemtime( get_stylesheet_directory() . '/style.css'); ?>" type="text/css" media="screen, projection" />
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