Hi Nacho,
Cornerstone comes free when using X theme because it is a required plugin. It will/should work as long as X theme is validated. For other themes we have to use/buy standalone Cornerstone plugin. If you have the standalone Cornerstone, feel free to use it with other themes.
Regarding your original issue with the plugin when using it with X theme, we need to check it. Unfortunately, I can’t access at the moment. Staff is available 24/7 but we are on different location. Now we know that the issue is theme related. We still need further investigation.