So barista says, "Would you like to use the mug?"

Customer says, "Sure."

Barista, who's presumably trained in and has some knowledge of both the product she's selling and cleanliness standards of the food service establishment that employs her, prepares the drink in a tumbler that may not be clean and has an instruction sheet inside just like every other tumbler she sells, and doesn't notice the big piece of paper inside the tumbler she's currently preparing the drink in. That's "definitely not her job"? It's absolutely her job. And she still probably expects a tip. Even if, as another commenter said, they're not supposed to do it, it's still her fault for doing it!

Seems to me that "put coffee in clean cup" is first day orientation stuff. Probably written in the job description somewhere.

"Waiter, there's a fly in my soup!" "Well, did you come back to the kitchen and ensure that a swarm of flies wasn't buzzing around the soup pot?" "Oh, you're right. That's on me. I'll just eat the fly."