Sorcerer Dragon Mage Passive Secondary Casting Skills

I am playing a build that is casting elemental nova via Frost claw, and I have several points put into the Dragon Mage passive.
The Dragon mage passive says:

You are granted increased damage with an element whenever you have casted a spell of another element recently (last 4 seconds)

It is my understanding that, Because “direct” is never explicitly stated here, that it should work on secondary casted spells. (Such as one spell casting another). This is however Not the case, Any casting of elemental nove through frost claw, does not trigger this. If I cast Elemental Nova myself, then it triggers as expected.
This is also applicable to Black Hole’s Armageddon as a second example.

If the intention is for Dragon Mage and Dragon Breath to only trigger on direct casting, then It isn’t conveyed through the wording, since other nodes on the passive explicitly state direct casting as a requirement.