Hi Robert, thank you for contacting us!
The detection script in W3TC requires mod_php mode to detect if modules are available, and that mode is not available to the plugin if you are using PHP-FPM. However this only means that W3TC cannot detect them, they are still available for use on your server.
For example, enable Gzip compression (which requires mod_deflate) check if Gzip compression is working by testing your website on GtMetrix or any other Gzip check tool. The reports from those services should indicate that Gzip was used to speed up your website, even though W3TC couldn’t detect it in the compatibility check.
Please let us know if you have any additional questions for us!