As your service is based on CloudLinux you have full control over module installations per each of your domains.

To enable MySQLi for you domain please follow these steps:

1. Login to the cPanel of your domain. (This is the cPanel of that domain not the main WHM account)
2. Click on "Select PHP Version"
3. Change to PHP version to anything that is not native and click on "Set as Current"
4. Then from the list of modules check "ioncube_loader" and click on Save