No, I think most people autmatically know that when you are talking about time quarter = 15 minutes. I mean if you've ever seen the face of a clock it is obvious that every quarter has 15 minutes/3 hours represented.
I think there is a generational thing developing here, as many younger people are much more familiar with digital time than analog (clock face) time, so they don't automatically think in terms of quarters. I was able to find some forum discussions where people said that they had trouble using analog clocks or knew an adult who could not tell time on an analog clock.
I remember having trouble when I learned German--had to remember that "half neun" (half nine) was 8:30. Halfway to
nine, not half past nine.