I guess by quest you mean duty, as in duty finder. It does give a warning that when withdrawing 3 times from a duty you will get a penalty, and that includes all party members that were queueing that time. If you still withdraw after the warning then... up to you. Those are the rules.
Saying it like this "penalty from quests that we haven't even started" makes it sound like a bug, when all you did (or that person) was click the withdraw button ignoring the warning on a duty finder instance.