Thank you for this.
I actually did go in to another connected City and was concerned to see that, not only was the GW progress not registered, that the GW hadn't even started yet!
However, given my knowledge of Region sync, I decided to wait a few game hours and the GW did update itself.
Am I not able to ask each City to contribute something? I've started a second GW in another Region and have one City contributing Oil but I want a second City to contribute Alloy as the first City doesn't produce Alloy.