Here is the tray icon.
I am not doing anything in particular when it spins, it just starts on its own.
How do I know the program is doing daily updates?
The icon never just spins on its own, there is some ativity on your system and that activity causes avast to scan that activity, this in turn causes the icon to spin.
You can temporarily enable 'Show detailed info on performed actions' in the Standard Shield, Customize, Advanced, see image. Let us know what is being scanned (some general examples).
The Web Shield and Internet Mail providers also can have this option applied should this not reveal what is being scanned.
It depends on your Program Settings, Update (Basic), the default is Automatic and you should be informed in a pop-up at the bottom right of the screen that an update has occurred.