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^ except I move back to position immediately after I go behind the mob.
I actually don't wait for cast bar to finish... Because even though 2.1 supposably fixed delay, it is still there.... So I just pre-move before the cast animation finishes (roughly 85-90%). Maybe it's because of latency
I never move through the mob, I strafe, but it just seems easier for me. Melee dps that move because of that are just used to bad tanks, or are just doing positional stuff like using Twin Snakes on a Monk.
I run through the mob. As soon as the red indicator is gone you can run back through the mob since the action has already been queued by the server and the positional update will recognize you're not in that area. A good example of this is like on the Ultima fight where you have to do the in/out motion. The screen shows you're running into that plume but since the action has already gone off and you weren't in it when the positional check was placed, you don't take any damage.
That's also true with Landslide Btw. Feels awesome to have Titan striking the ground and you effortlessly withstand it (although you never are in danger).
I usually just dodge and once the red cone is over I step back in. Once the animation finishes, I'm back where I was. Think Ninja
You can move in during the attack animation. If you do this correctly the mob/boss shouldn't move at all.
If melee dps cant move and attack then somethings wrong.
Most of the replies here are very good in response to the main subject, but I'd like to throw an additional piece of advise. If you dodge to the left, right, behind or whatever, and the mob turns to your position, I have found that it's best to just keep it there instead of correcting your position, otherwise the DPS will over correct. I've done it many times on my Paladin and only realized it was annoying when I leveled up a Dragoon, where positioning is key to keeping a good rotation going, especially in the later levels.
I have found that just bringing it up in party chat with a brief "I'll dodge AoEs running thru the boss/mob and back in place" or something similar, helps the DPS to know you aren't going to put them in unnecessary harm's way. Or when it is happening, throwing out there a "You don't have to move if you don't want to; I'm moving back in place each time" in party chat helps as well.
Moving through the mob/boss versus slightly out of the way and back also changes in different circumstances: sometimes you can't move slightly out of the way and stay there and run back in place (such as 2+ pugs in WP at once) no matter how good you are, because each mob's AoE starts/ends at different times. So you may have to move 3 times. Or worse, running through the 1 mob's AoE, causes the other mob's AoE to face the other way so no one dodges anything, and could even hit the healer.
In addition to the above:
IMHO, it just comes down to letting people know your plan. Trusting they will catch on doesn't always work. Letting them know your plan pretty much always does. And since it only takes about a minute to let everyone know, it makes it easier for all. Additionally, the DPSers or healers may be tanks themselves and do it one way and think that's the way you are going to do it. Always helps to clarify.