If a plugin is installed, up-to-date and activated you will see the Learn button next to it in Astute Manager, this button is quick access to the associated plugin training material hosted on this site. This button doesn't affect the local state of your plugin installations. You can read more about this here.
When you install our plug-ins they won’t show up in Illustrator automatically, they will be added to your toolbox panel in Illustrator. If you do not see the Astute Graphics tools in the toolbar, please ensure that you are using the advanced toolbar by selecting Window > Toolbars > Advanced. You should be able to tell if a plugin is installed by checking the Illustrator, Window and Effects menus.
If you have recently moved to Illustrator 2020, please ensure that you look for new instances of Ai in the settings panel of Astute Manager (advice on this here). For full instruction on installing, please see How do I install with Astute Manager?