You need to add status = 1 to SQL part:
$this->db->query("INSERT INTO " . DB_PREFIX . "reviews
SET author = '" . $this->db->escape($data['name']) . "',
customer_id = '" . (int)$this->customer->getId() . "',
product_id = '" . (int)$product_id . "',
text = '" . $this->db->escape(strip_tags($data['text'])) . "',
rating = '" . (int)$data['rating'] . "',
status = 1,
date_added = NOW()");