Make updater register the tray app for auto-start.
The updater should be able to install the tray app in the All Users startup folder (C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Startup)
See https://stackoverflow.com/questions/9701840/how-to-create-a-shortcut-using-powershell on how to do this with PowerShell.
See also #2 (closed), #13 (closed)