To make a remote connection to the server you must add the IP address of the server you are trying to conenct from to the list of 'access hosts' on the 'MySQL databases' page of the account cpanel.
Once you have added the IP address you will need to re-add the users to the databases to ensure the correct access permissions are applied.
To connect to the server you would use the account domain name or IP address as the hostname and the database user name and password that you created on the 'MySQL database' page of the cpanel