There's a few varying opinions here in regards to Druids, so I thought I'd take one for the team and buy the thing just to get the truth. I'll just state what I found and let you decide if it's worth the Emblems or not!
- It procs on HoT ticks!
- It procs on direct heals.
- It will proc regardless of who the heal is on.
- It does NOT proc on HoT ticks that were 100% overheal, but direct heal overheals can still proc it.
As an exception to the above, the bloom from Lifebloom cannot proc it on an overheal, despite the overheal appearing in the combat log like a direct heal (unlike HoT ticks).
There is a difference between the trigger on this trinket and "on spell hit/cast" trinkets/talents like Valonforth's Remembrance. For example where that trinket will proc on the initial casting of Rejuvenation, the Egg will only proc on the actual ticks.
As expected there is an internal cooldown, the quickest I could get two successive procs was 48sec using Lifebloom.
Update: For the life of me I can't get this to proc on Swiftmend, overheal or otherwise.