This is a issue with the browser cache and not a hosting issue
The web browsers will cache the old version of the css and ignore the updated file
You can try to clear the browser cache but some browsers are really stubborn and still refuse to update
The best thing is to use a new file name when you make a change css001.css css002.css etc to force the browser to use the new version
I also had this same issue and I ended up having to write a small bit of php code to handle this automatically without having to make changes to filenames and pages, see this link below