Now it's becoming interesting and really confusing. I had some time to dig through a little. Looks like that update-notifier can be configured through gsettings/dconf-editor (see the related attached screenshot). So, update-manager has nothing to do with notifications but it's update-notifier which runs update-manager.
There is no way to configure update-notifier through it's own GUI and at the same time update-manager's settings are ignored by update-notifier.
Now it's becoming interesting and really confusing. I had some time to dig through a little. Looks like that update-notifier can be configured through gsettings/ dconf-editor (see the related attached screenshot). So, update-manager has nothing to do with notifications but it's update-notifier which runs update-manager.
There is no way to configure update-notifier through it's own GUI and at the same time update-manager's settings are ignored by update-notifier.