To make Permalink Manager compatible with Postie plugin, you will need an additional code snippet. After the new post is created, the custom permalink will be regenerated and a final title and slug will be used in the URI.

function pm_regenerate_the_permalink($post) {
	global $permalink_manager_uris;

	// Get the default custom permalink based on a permastructure set with Permalink Manager
	if(!empty($post->ID)) {
		$permalink_manager_uris[$post->ID] = Permalink_Manager_URI_Functions_Post::get_default_post_uri($post->ID);

		// Save the update
		update_option('permalink-manager-uris', $permalink_manager_uris);
	}
}
add_action('postie_post_after', 'pm_regenerate_the_permalink', 99);