That would be controlled mainly by their cached files, and their cache file settings.
You could possibly add a few lines to your htaccess file to give your site some control over how it requests others to cache your files, but ultimately, their cache is prority over whatever you tell it to do.
Add this to your .htaccess file -
<FilesMatch "\.(ico|pdf|flv|jpg|jpeg|png|gif|js|css|swf)$">
Header set Cache-Control "max-age=1209600, public"
</FilesMatch>
But the best way to control that your users see your most up to date header image, is just to use a different file name when you change the image.
If your current header image is name "201412.jpg", and you want that image to refresh for everyone in January, edit your header and use "201501.jpg". At first, no one will have that file in their cache, so it will be requested from the server. Then use "201502.jpg" for February... and so on.
