I 've had the same issue, especially with installations with password protection on the web interface.
You need to submit a few additional parameters to the Tray icon shortcut:
Duplicati.GUI.TrayIcon.exe --no-hosted-server --server-datafolder=<path_to_Duplicati-server.sqlite> --read-config-from-db
Copy the shortcut to C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Startup for auto starting the tray icon when any user logs in.
In the Duplicati Web UI, go to Settings and enable Prevent tray icon automatic log-in if you want to specify the access password when you use the tray icon to access the Web UI.