Corrupted Ether event
Kill all 3 elemental chieftains. Each chieftain will drop a handful of corrupted ether orbs which will slowly be absorbed to a chained servitor. Destroy every orb before it reaches a servitor. After destroying all ether orbs, the event will become heroic
Rift generator event
I have tried many times and I believe the way to trigger a heroic is to kill the 3 abominations and destroy the blights that spawn. At this point 3 Taken wizards will spawn which will also need to be destroyed. When you are transported to an ascendant realm, it is heroic. You will then have to kill one final taken boss. (The generator you protect may or may not have to be above a certain percentage)
I joined in real quick before work and today was the only time the heroic versions were triggered, after all the time I spent during the weekend