Hi,
Thank you very much for the details, it makes my work much easier.
I believe you are trying to search for products, but the plugin was not configured to look for the ‘product’ custom post type. I’ve made the change on your back-end: http://i.imgur.com/goscwFn.png
Now, it will return products.
You can check the following chapters in the documentation about general configurations:
– General Settings
– Searh in custom post types