I've gotta agree: if it's your first time running the dungeon, tell your party that. Even if you've run it a dozen times as a Dragoon, if you're tanking it for the first time, you tell your party "Hey, it's my first time tanking this dungeon. I know the fights, but bare with me here." It's just common decency, and 90% of the time people will be okay with it. And it also sets a good example for the others, because a lot of times the other party members will chime in if they're new, too, and that openness makes the run feel much nicer.
I understand that for vets in Coil or against HM Primals it can be a slog to have to re-explain everything for the thirty-seventh time, and you just wanna run through it as quickly as possible. But if I'm gonna be completely honest, those couple minutes you spend explaining the fight may very well mean you don't waste the next 30 wiping before a victory, and can be well on your way through your second Titan fight.
A perfect example was when a FC member and I were farming Myth tomes in AK and WP for a couple hours. Neither of us had Allagan pieces or Myth gear, so we weren't planning on speed runs. Well, lo and behold we get into WP with a WHM and SMN decked out in Allagan pieces and Relic+1's. They ask us if we're doing a speed run, and we casually answer, "Sure, why not?", which we meant as 'quickly kill everything and unlock the doors ASAP.' Well, those two weren't pleased with us because we didn't kill the first two Tonberries fast enough, nor anything else, and they proceeded to insult my friend until we killed the first boss. He got fed up and left, and they followed soon after. Not a minute later the party fills back up and we complete the dungeon about five minutes before their lockout timers are up--not speed-running, and I think we actually wiped to the flan boss, too. If those two hadn't been "MYTH TOMBS NAO!!1", and had been just a little more patient we'd have all finished the run without a fuss, and they'd all be running again.