The content doesn’t get imported on custom importer / plugin activation script

I’m working on a starter sites plugin. It’s based on One Click Demo Import script and native WordPress plugin-install.php and wp-admin/includes/class-wp-upgrader.php. When you select a demo, it shows the list of required plugins and if these plugins are installed or deactivated. The importer works well when the plugin is not installed but doesn’t import content properly when the plugin is deactivated. Posts and pages content gets imported, but Contact Form 7 forms are not.

Here is the logic that is responsible for plugin installation / activation. Not sure what I’m missing here.