How to backup the Publisher Star HD app data to iCloud?
You will be able to locate the iCloud settings for this App with these steps:

1. On the device, open Settings and select "iCloud"
2. Select "Storage & Backup"
3. Select "Manage Storage"
4. Under the first section, "Backups", select your device
5. Under "Backup Options," please make sure the switch next to "Publisher Star HD" is set to ON (blue). If you do not see "Publisher Star HD" in the initial list, tap on "Show All Apps"

The following official links provide helpful detailed information on iCloud backup and restore: