Hi,
It should work okay, if they show up on the search back-end. As far as I know, CPTUI does a great job adding taxonomies and post types.
A very common issue is, that possibly results, that does not belong to any of the selected taxonomy are displayed as default. I suggest trying to change this option, to see if it makes any difference: https://i.imgur.com/LMJiq0I.png
