Having Views searchable by users I would like to be able to search my views by a field that is generated by an Entity Reference of users of the site.

Attempt #1 - Combine Fields Filter
I added this filter as exposed with the setting of "Contains" either from the "Title" field or the "Responsible Party" field (which is the Entity Reference field that is a list of users.  Here is a picture of the settings
The results of this were that the title field is filterable as pictured here
Yet the user generated field did not properly filter as shown here  

Attempt #2 - Search: Search Terms filter
Same process and same issues using this filter.  Here is a picture of the settings  

Then the same results as shown here.
Searching Title 
Searching Users
Looks like you did all the steps correctly, How To Create Combined Search Filters In Views?, which leads me to believe that this is a bug. 

Upon looking at the View's issues, I found Combined fields filter not working with entity reference.

Therefore, you will have to use it as a standalone, not combined, filter until this bug is fixed, which does not look like it will be any time soon.