The only reliable way to ensure that everyone reloads your new file is to change its URL. A smart way to do this without renaming it is to apply to a random string:
<link rel='stylesheet' href='/mystyles.css?random=87365835'>
That, using a sledgehammer to crack a nut, and bypass all the HTTP mechanisms that exist for this, but it will work everywhere, while other methods have caveats.
: @jitter: URL- - CSS , , CSS .