iCloud back up for iPhone

You can use iTunes on a computer to control the option of whether the phone automatically backs up to iCloud. That option can also be turned on or off directly on the phone without connecting to iTunes. There is no other involvement of a computer in doing an iCloud backup, and no need to use the computer at all. Changing the setting on the phone via iTunes on the computer does not actually start the backup. If automatic backup to iCloud is turned on, it will happen while the phone is charging if wi-fi is available. See the following from How to back up your iPhone, iPad, and iPod touch - Apple Support for the iTunes screen where you can change the automatic backup option: