For the search phrases Add On, the list of search phrases are stored in the database to allow fast query of this data.
This data is re-generated one of two ways:
1) Open this link:
http://www.YOUR_ADMIN_URL?dispatch=quick_search.generate_catalog
(replacing YOUR_ADMIN_URL with your sites admin page URL)
2) When a new product is added to the product catalog via the "Add Product" functionality, the data is re-generated automatically.