Agree on the basic conditions for criteria for all stories.
This 'meta' conversation needs to be had. It doesn't arise of its own accord, not being related to a ticket.
This is where leadership (at all levels) comes in.
Take charge of the situation, organize the meeting, get an agreement and then live by it.
The result of this is that future discussions can now be about the agreement, if its being met, if it needs to be changed, rather than trying to raise an issue about any given particular story.
Making something up, it could be:
- initial data state required
- user taking action
- expected result
- happy and sad cases
Make sure the Behavior of users is the Driver of the Development process
See also https://www.mountaingoatsoftware.com/agile/user-stories for Mike Cohn's take on user stories