Exclude taxonomy term from view display except its own?
You seem to be on D7 and using the default Taxonomy term Views. 

Out-of-box Taxonomy term Views is set up to cover all taxonomy Vocabularies you create on your site. 

You can override this to "split" that functionality into more than one View, that have different settings, and control which Views is responsible for displaying which Term pages. 

BTW I find it best to disable the original Taxonomy terms view, Duplicate (Clone) it and work on the Duplicate so I always have the original to reference back to. 

On D7 this is usually done with the help of the Taxonomy display module although this module only provides a convenient interface for adjusting each term, but it doesn't provide the "splitting" on the Views level. 

You'll have to create the second View yourself, and edit the original Taxonomy term views to exclude that special term yourself. 

In the original Views you can add another Contextual filter, set it to the fixed value of the ID of your xyz term, and under More set to Exclude. This way no articles tagged with this term will appear on other term pages. 

Clone the Taxonomy terms Views, name it meaningfully, and override values for the Contextual filter to only show content for the xyz term (I'm guessing ti will again be the fixed default value, but without Exclude).  

You mention regions and themes a lot, but that is not how you usually control filtering in Views. So if you have more than one View listing content where you want to exclude the special xyz tagged content, you'll have to edit each view to filter out that content. There is no easy way to filter according to theme regions that I'm aware of.