Why avast update on window shutdown instead on boot-up?
If an update happened close to your shutdown, this is / was a coincidence.
Agree with ady4um, if you had a VPS update on shutdown it is nothing more than coincidence, 4 hours (or whatever period you have set) after the last update check.
Avast does check for VPS updates very shortly after boot, when an internet connection is available.
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If however, you are asking why doesn't avast update on shutdown, then I would counter with why when it is available shortly after boot ?
Most people when they shutdown their system don't want to be sitting around for updates, etc. they just want it shutdown.