Thanks for the reply, joy.
I have attached screenshots in this google photos album to demonstrate what I am referring to.
https://photos.google.com/album/AF1QipN0fozcRdOLNGyuLDeuB0bBCS1g6tsKurnCho4I
The information from the screenshots shows, via query monitor, that one site is using page.php and the other is properly using taxonomy-product_cat.php. I have made no changes to the backend of the sites, other than the problem site has been updated.
Does this provide you with any further insight into this problem?