Often times the dps/healers who pull ahead of you are simply more experienced players, likely tank mains, who do it because they see the party is capable of handling big pulls just fine and you're doing single pulls, slowing everybody down for no reason.
Outside of very rare situations, this game doesn't really have any strong trash mobs that need to be CCd or focused down, so it is in your best interest as a newbie tank to learn how much to pull in each part of every dungeon and how to peace your cds for said pulls. If you're doing your pulls right then people won't be pulling ahead. If you don't know yet how to pull and people grab extra mobs - don't be a princess and just get the mobs off of them. The whole "you pull you tank" mentality usually just wastes everybody's time. You're here to make the run as smooth and comfy for your group as possible, that's your job as a tank.

One extra tip though - don't stop for a bit after pulling and then run to next group or start next pull before the mobs are dead. Former will often make people waste their placeable heals and AoE, while the later doesn't let people take advantage of the few tics of out of combat TP/MP ragen(which usually takes care of any healer mp issues btw, so long as you actually let them get out of combat).