Hi!
The problem was simply a missing configuration 🙂
On the Search instance general options panel the “Index table engine” was not selected, nor the option to search within products: http://i.imgur.com/8dvlt2k.png
Individual search instances need to be configured independently from the index table configuration – as they can have different configurations as the index table itself.
I’ve selected the product custom post type and the correct engine, now it should display results correctly.