Each tank has a signature AOE ability. Waiting for this ability before doing AOE damage is not a guarantee that you won’t pull aggro but not waiting for it is generally a guarantee that you will.
The main warrior AOE threat tool is Thunderclap. It is a short-range, instant AOE. It looks like this:
It makes a sounds like a lightning bolt and can also be identified by the cracked ground effect it causes.
The druid AOE ability is called Swipe. It is also a short-range, instant AOE. Here are before and after pictures of what this looks like:
You can tell this has hit because all affected mobs will briefly turn red.
Paladins have an ability called Consecration. This is a short-range area effect centred on the paladin. It looks like this:
The yellow sparkles on the ground are pretty identifiable.
While Frost death knights might not always use this, a DK tank can usually be expected to cast Death and Decay. This is a short-range area effect, though unlike consecration it can be placed on a specific spot. It looks like this:
Look for the giant red circle on the ground.
What have we learned?
Your randomly-assigned tank will appreciate it if you wait for them to do one of those things before raining fire, ice, arrows or knives on top of your enemies.