Compatible with the WooCommerce Product Search plugin?

I’m using the WooCommerce Product Search plugin. This plugin has a live search function whereby matching products appear in a dropdown as you type. If you press enter then you are taken to a search results page.

When running a search, products that should not be visible to the current user appear in the search. If you press enter during the search, the search result does not include the non-visible product, but the results page shows a results total that includes the non-visible product.

I realise that the issue most likely lies with the WooCommerce Product Search plugin, but thought I should post here in case there is something that can be done within this plugin to make it compatible with that plugin.