Backing up in iTunes and backing up in iCloud are two very different processes...essentially, your computer and iPhone are doing the back up properly if it is in iTunes and is backing up directly to your computer, as iCloud is only used for a backup directly from the iPhone itself (which is why the controls are also on the iPhone itself).
If you open iTunes, you will see a prompt of options for backups...automatic backups give you the option for iCloud or the computer (and these are done in an automated way so that you don't have to bother "remembering" to do them)...or you can manually back up your device in iTunes, which does so onto your computer (with no option for iCloud).