We do have custom module that we have created. These modules are precompiled when publishing to our servers.
Perhaps this might be the issue. In version 9.0.2 or less, we usually deployed our site with the setting "Precompile during publishing" using Visual Studio.
With this new version 9.4.4, this precompile setting seems to be generating the error mentioned above. When the precompile setting is unchecked the error message is no longer an issue and the site seems to function properly but with the .cs file present.