Thanks for your feedback.
The problem here is the field type is
taxonomy_advanced. This field does not setup a relationship between posts and terms. Instead, it only saves terms’ IDs in the custom table (or post meta if you don’t use custom table).
To setup the correct relationship between posts and terms, please use field type
taxonomy. In this case, the plugin does not save any value. Instead, it only sets the post terms. And thus, the WordPress counter works correctly.