Like mentioned here: https://dev.to/timgeyssens/ow-you-need-to-clear-your-browser-cache-to-view-the-changes-never-again-with-umbraco-cms-3p7e
Not sure if that is the easiest way... but just if changes are made to css/js when you deploy them... the client browser cache should be updates so it doesn't show a strange mix of new markup with old styling