The easiest way as far as I know to force all browsers to re-load the updated css is to make reference to css version in the theme file. This is of course applies more widely, but specifically in Omeka S, I suppose that you have a pointer to your css file in themes/your_theme_name/view/layout/layout.phtml (obviously replace your_theme_name with the folder name of your theme).
If you are really just editing style.css, just replace style.css with style.css?version=01 wherever it is mentioned there. And remember to bump version (style.css?version=02 , etc.), every time you deploy your updated css.
Editing the original css file is likely to cause issues when you will eventually update the underlying theme.
A slightly less invasive option even without bothering with sass is to have a “custom.css” file, and have it loaded after the others at the end of head. So just before </head>, add a line with something like: