Hey @dakinimonica,
The plugin will work on product archives/categories and also on single product pages.
If however, the developer of the WordPress theme you’re using has modified the single product template of WooCommerce by overriding that from within their theme that can stop the plugin from working.
A way to test if that is the case is to temporarily enable a theme like Twenty Twenty or the free Storefront theme and check the single product page buttons.
If the behaviour persists with one of these themes activated try deactivating all plugins aside from WooCommerce and WooCommerce External Product New Tab as it could be another plugin on your site causing this too.
I hope this helps.