How to get view by tag sorting the same as main view sort criteria
You can add another argument/contextual filter (surename). And in the contextual filter settings you could specify the sort criteria when the filter is not in URL. You can choose the sort criteria numeric or alphabetical as in the screen shots 

Then 

Edit: If you have a content type called directory, and the content type has taxonomy term reference and a field called surname you can replicate the config in the screen shot below and it should work. Note contextual filter and sort criteria settings:
 1. Page View config note:
 
 2. Contextual filter taxonomy tag settings
 3. How the it will display the summary: 
 4. How it will display the content, note how it is sorted by surname