Keeping Backup by Zaweba running in the notification area
How Backup by Zaweba keeps schedules running from the notification area when you close its window, how to quit for real, and why one copy runs.

Schedules only work if something is awake to run them. Backup by Zaweba uses its own scheduler rather than Windows scheduled tasks, and that scheduler runs while the main window is open or while the app sits in the notification area at the end of the taskbar. Knowing how the app moves between the two saves a lot of puzzling over a backup that didn't happen.
Closing the window isn't quitting
When any of your pairs has a schedule, closing the main window keeps Backup running in the notification area. The dashboard disappears, but the scheduler carries on, so a daily run in the evening or a pair set to run when its drive is connected still fires.
This behaviour has its own setting. Tools > Settings includes a box labelled Closing the window keeps Backup running in the notification area when any pair has a schedule. Leave it on if you rely on schedules. Turn it off only if you'd rather every close be a full exit and you run your pairs by hand.
Quitting for real
To stop the app completely, use File > Exit (stop schedules). The wording is deliberate: once you exit, no schedule will run until Backup is started again. A daily or weekly slot that passes while the app isn't running isn't lost, though. It runs once as soon as the app is running again, and a restart won't repeat a slot that has already been handled.
One copy at a time
Only one copy of Backup runs at once. If it's tucked away in the notification area and you start it again from the Start menu or a shortcut, the existing copy simply brings its window back up rather than a second one starting. That keeps two schedulers from racing each other over the same pairs and the same drives.
The command line follows the same idea. When a script asks Backup to run a pair with --run while the app is already running, the request is handed to the running copy instead of starting another.
Notifications while hidden
A trusted pair, one marked Run without preview, runs in the background on its schedule and lets you know with a notification. When the window is hidden those notifications appear as a balloon from the tray icon. A pair that isn't trusted stops at its preview on a scheduled run and waits for you, so open the window now and then to see whether one is waiting.
The tray icon has a menu of its own, which includes Send feedback.
Starting with Windows
The notification area is where Backup lives between runs, and Start with Windows is how it gets there after a restart. Tick Tools > Start with Windows, or the matching box in Settings, and the app starts quietly in the notification area each time you log in, so schedules keep working without you opening anything. It's a per-user startup entry, so it applies to your own Windows account.
Put together, the setup most people want is simple: a schedule on each pair, the closing setting left on, and Start with Windows ticked. After that, Backup by Zaweba stays out of the way and the dashboard is there whenever you want to check on it. A green tick on every card, and a header that says all your backups are up to date, is the sign the background scheduler is doing its job.