Actions don't work for triggers created by LLD (from template) when action uses a condition: Host template = "Template_with_LLD"

Situation: LLD discovery rule (with items and trigger prototypes) created in some template. This template is linked to some Host. Real items and triggers are created and they work well.
Using the condition Host template = "Template_with_LLD" it's regular practice. Even for the items+triggers created by LLD. Yes?

But in such situation the actions don't work.
It's happened because trigger (created from prototype) "is inherited" not from template and from Discovery rule (which respectively inherited from the template). IMO.