When non-security updates are available, Update Manager should open automatically whichever is later: (a) X days after it was last open, whether that was manually or automatically, or (b) X days after updates were installed by any apt-powered method. X should default to 7.
When security updates are available, Update Manager should open automatically whichever is later: (a) Y days after it was last open, whether that was manually or automatically, or (b) Y days after updates were installed by any apt-powered method. Y should default to 1.
So yes, it is intentional that running apt-get update shouldn't cause Update Manager to open automatically. If you run apt-get update manually, it's highly likely that you're about to install updates manually too, in which case you don't want Update Manager getting in your way.
When non-security updates are available, Update Manager should open automatically whichever is later: (a) X days after it was last open, whether that was manually or automatically, or (b) X days after updates were installed by any apt-powered method. X should default to 7.
When security updates are available, Update Manager should open automatically whichever is later: (a) Y days after it was last open, whether that was manually or automatically, or (b) Y days after updates were installed by any apt-powered method. Y should default to 1.
So yes, it is intentional that running apt-get update shouldn't cause Update Manager to open automatically. If you run apt-get update manually, it's highly likely that you're about to install updates manually too, in which case you don't want Update Manager getting in your way.