Watch - setting 3rd party complications from phone?

Am I imagining that we can set third party complications from the phone, as long as the app is installed? I can scroll through and pick 3rd party complications from the Watch face, but on the phone I can only choose the standard Apple complications. I could swear this limitation wasn’t there on my previous Watches, so I’m wondering if my install is messed up.

If it’s a new watch the apps may still be installing. It took a good few hours for mine to sync over and then there were still apps that I had to re-add manually.

The other point of note is that new complications require an app update from the developer to work. I know CARROT and others have done this, but some app developers haven’t yet had a chance.