I play Paladin and, as a tank, you pretty much are the leader of the run, because you are the one walking ahead, marking mobs and controlling what's killed and when. But, you're only 1/4 of the party, there're 3 members remaining, so I call for democracy always. If it's a low level dungeon, I ask the party members what they want to do: Kill everything or quick run. If the majority of the players want to kill everything, so bet it, otherwise, I'll optimize the run to have a quick clear.

Who's fault here? Hm, it's divided between the DPS and the tank. The DPS for acting like a child and leaving and the tank for not giving his opinion. The tank should have said "Bro, I don't feel comfortable with doing a full clear because I'm in a hurry. I'm sorry" or something. Comunication is key for these issues.