Q: Etched sigil + Firebird - not trigger?

Have a question. I am playing wizard over 99% of my D3 career.

Now i wanted to try 6 piece set bonus of Firebird with Etched sigil automatic tornadoes (fire rune).

But it looks like these tornadoes do not trigger 6th piece set bonus? Even when i cast them manually? Is that possible? Cast fire energy twister to burning enemies from firebird is not considered as “hit”?

It’s probably not counted as a hit if you cast the fire tornados. And the tornados from etched sigil don’t trigger too either because they’re procs (and procs don’t proc or something) or they’re unruned. Etched sigil is only good for T16 rifts together with the bracers Ranslor’s Folly because they pull monsters together so you can blast them (and you don’t use Images with that build).
You can see suggestions for different builds here:

When I farm with the nephalem rifts build I use Meteor shower as one of the skills because it procs the 6 piece set too.