Can you copy and paste your header response parameters from the request?
I loaded up my Kentico 10 base install, and added a CSS link:
/CMSPages/GetResource.ashx?stylesheetfile=/App_Themes/default/CMSDesk.css
Here's my headers
Cache-Control:public, must-revalidate
Content-Disposition:attachment; filename="CMSDesk.css"
Content-Length:76439
Content-Type:text/css
Date:Sat, 18 Mar 2017 15:05:57 GMT
ETag:"file|11/21/2016 5:32:00 AM"
Expires:Sat, 25 Mar 2017 15:05:57 GMT
Last-Modified:Mon, 21 Nov 2016 11:32:00 GMT
Server:Microsoft-IIS/7.5
X-AspNet-Version:4.0.30319
X-Frame-Options:SAMEORIGIN
X-Powered-By:ASP.NET
When i add the web.config key and set the expiration to 60, this is what i get:
<add key="CMSPhysicalFilesCacheMinutes" value="60"/>
Cache-Control:public, must-revalidate
Content-Disposition:attachment; filename="CMSDesk.css"
Content-Length:76439
Content-Type:text/css
Date:Sat, 18 Mar 2017 15:09:41 GMT
ETag:"file|11/21/2016 5:32:00 AM"
Expires:Sat, 18 Mar 2017 16:09:41 GMT
Last-Modified:Mon, 21 Nov 2016 11:32:00 GMT
Server:Microsoft-IIS/7.5
X-AspNet-Version:4.0.30319
X-Frame-Options:SAMEORIGIN
X-Powered-By:ASP.NET
As you can see, the expiration web.config is behaving as expected, it changed from 10080 to 60 minutes for the Expires tag... not sure why it's not working for you, what version are you on?