While it may be your first time in the dungeon, everyone else in the group has likely done it at least 5 times. To most of us it is a chore to be done as quickly as possible. So yes, tanks are going to pull wall to wall, and you are expected to learn how to heal through it. It will not be stopping once you get to higher levels, the expectation will just get larger. Single pulls in dungeons don't do enough damage to warrant a healer anyways(this is more true at higher levels), so you'd actually be stuck either overhealing or doing a very boring damage rotation.