Target logic based on Widget / Sidebar Name

You can write the logic inside widget functions. When the widget is added in sidebar, it will check for sidebar name and home page.

   global $wp_registered_widgets, $wp_registered_sidebars;
   $sidebars_widgets = get_option('sidebars_widgets');
   if($sidebars_widgets["sidebar-1"] && is_home()) 
   {
      //Write your logic here
   }