Mina Dimyan frequents a Stamford, Conn., cafe, where he orders a cup of strong coffee for $3. It comes with a splash of guilt.

The clerk swipes Mr. Dimyan’s credit card and then swivels the store’s white iPad around. There is an uncomfortable pause. Prompts on the screen ask the 33-year-old human-resources recruiter to sign his name and pick a tip: 18%, 20%, 25%, a custom amount or “no tip.”

“It’s...