Third-party contact list

I'm having such a problem with robocalls that I have to do something. I found a post which talked about enabling "do not disturb" and allowing contacts through and another suggestion of assigning a ringtone to contacts and setting your default ringtone to a silent ringtone, both of which I like.

Here is my problem. I have a third-party app which has a contact list and the phone tells me who is calling if the person is found in the app and not my contact list.

I want either to assign a specific ringtone to contacts in that app or allow "do not disturb" to let numbers in that app ring through as well...or both.