Where and how are you including your CSS? Maybe you can probably add something like ?v=20160515 behind your css link.
<link href="~/CMSPages/GetResource.ashx?stylesheetfile=/sitename/assets/css/style.css?v=20160506" type="text/css" rel="stylesheet" />
Small side note:
We use a customer specific template css (as shown above), which they cannot change. Then we add an extra css file where they can fiddle with some css classes and stuff. I'm sure there are other ways but this is the one we are using atm.