I noticed that in order for the OmniFocus watch app to always be up to date I obviously have to launch OmniFocus on my iPhone once in a while. I think I heard on MPU or Automators that mcsparky had a way to launch OmniFocus first thing in the morning in order to have everything updated.
I tried to recreate this behaviour through automation in the shortcuts app but always get “Failed to run automation”. This is run time based, which works fine if I have the phone unlocked.
That DTTG sync question has been put to him a couple of times already.
Opening an app on the iPhone is a foreground activity, so I believe that would require the device to be unlocked.
It would be worth you checking that OmniFocus is enabled for Background App Refresh in the Settings app. That should generally ensure you stay up to date.