I have the same problem. But I have achieved partial results. What I did:
1. Updated my and our two children's iPhone to iOS 12. My wife's iphone didn't yet. Me and my wife is Parent user and our two children are Child (under 16) user. We are in Family Sharing for long ago.
2. Turned on Screen Time on my phone as parent user and after I turned on it on my kids phones as child user.
3. Their name did not appear in the screen time app and I did not control them. The app worked in stand alone mode. I checked this: Settings > My Apple ID > Family Sharing > Shared Functions > Screen Time. I found it turned off. But impossible to switch.
4. I did the following many times: devices soft/hard reset, Apple ID logout-login, Screen time swith off-on, etc... but nothing changed
5. It doesnt't changed for 2 days.
6. I updted my wife's device to iOS 12. Turned on Screen Time and to my surprise appeared the children's name in app. In my device too. It's too nice to be true...
7. I can not manage my son's device. The other one is perfect.
8. I did step 4. again. Unsuccessfully.
I have only one short question after I suffered several hours: ¯\_(ツ)_/¯ ?