Just create a file, say custom.php, with the content above and make a request through the webserver to it. It dumps the result, MIME type of the css file, into the error log.
I don’t know to what extent you control the server but if it’s shared hosting, just put the php and css file to the webroot and make them readable for the web server. Then you can execute by making a request http://www.domain.com/custom.php; check php log and remove files after the test.
If you have access to the command line, you can test how your system determines the MIME type directly, this shows if the problem is on the lower level, I only know the command for Ubuntu which I posted above.
Also, I found a similar thread that looks related: I have an HTML, with a CSS style shee - #16 by asmecher