Automatic works as described by the UI from my experiences.

For Windows users, make sure Bonjour is also installed and enabled as this is what iTunes uses to find your iPhone on the network. The PC/Mac and iPhone need to be on the same network, not an isolated guest network or similar.

Been using iCloud backups for a bit now, though the automatic WiFi backup is what I used for years prior. Yesterday I connected my phone to the computer for the first time, checked the WiFi box, and set automatic backups to the computer instead of iCloud. Disconnected the USB cord, dropped the phone on the Qi charger, and it started a backup (step 2 of 5 in the overall process here).

Today I used the phone for a bit, dropped it back off in the charger, and saw a new backup session starting automaticially. ITunes should also seek out phones on the network when freshly opened.