How do I generate formatted permalinks as specified in backend options?

Question

I searched everywhere for this but couldn't find any help. I'm working on a plugin that generates posts from a database, like so:

foreach ( $items as $item ) {
    $content = $core->parseTpl($item->Asin, $this->content);
    $titleColumn = $this->titleColumn;
    $postarr     = array(
        'post_content' => $content,
        'post_title'   => $item->$titleColumn,
        'post_status'  => 'draft',
    );

    $postId = wp_insert_post( $postarr );

    //more code...
}

When I do this, the generated permalinks look something like this:

http://mywebsite/?p=1190

However, I want the permalinks to look like specified in the WP-backend:

Using the wp_insert_post function doesn't seem to apply the permalink formatting. What do I have to do, so that my created posts have the formatted permalinks?