3👍
This depends a lot on the behaviour of S3 and the headers it sends when requesting files on S3. As you experienced, browsers will show different caching behaviour – so the best option is to use unique filenames.
I would suggest to use cachebuster hashes – in this way you can be sure that the new file always gets requested by browsers and you can use long cache-lifetime headers if you host the files on your own server.
You can for example create a MD5 hash of your minified file and append it (like mycss-322242fadcd23.css). Or you could use the revision number of your source control system. You have to use the cache buster in all links to this file, but you can normally easily do this in your templates where you embed your static resources. Depending on your application, you could probably use this Django plugin that should do this work for you.