Watch shows wrong time

I had this exact problem! Just got off a chat with Support and wanted to share my experience in case it helps anyone:

On my child's watch, under Settings/Clock - scroll to the bottom - the toggle for "Set Timezone Automatically" was greyed out and the wrong time zone was there.

On my phone (used to manage my child's watch) I turned off Screen time for my child:

Settings/Screen time/ scroll down to select family member / Turn off Screen Time

After a moment, my child could set the time zone on the watch!

Then I turned on Screen Time again, and everything still worked.

Hope this works for you!

Hello Apple-Help-Me-,

Thank you for participating in the Apple Support Communities! We understand that the time on an Apple Watch used by your child is incorrect. We'd be happy to help take a closer look at steps to take next.

To start with, are you able to change the time following the steps here:

Change the watch face on your Apple Watch - Apple Support

"

How to change the time shown on your Apple Watch

1. Open the Settings app on your watch, then tap Clock.
2. Tap +0 min. 
3. Turn the Digital Crown and choose how far ahead to set your watch. 
4. Tap Cancel or Set.

You can only set the time shown on the watch face ahead. Your alarms, notifications, World Clock, and any other times will still match the actual time."

If you're both part of Family Sharing, you may also want to check that there's no Screen Time restrictions for your child that could cause this behavior, such as "Don't Allow Changes" for Location Services. Keep us posted on the results.

Cheers!

Manage a family member’s Apple Watch

1. Open the Apple Watch app on the iPhone used to manage the watch.
2. Tap All Watches, tap a watch under Family Watches, then tap Done.

When you tap My Watch for a managed watch, you see a variety of settings: