Heartfire interaction with Guttersnipe et al

From Reddit:
If a permanent has a clause that would trigger upon reaching a requirement e.g
**Guttersnipe**
_Whenever you cast an instant or sorcery spell, Guttersnipe deals 2 damage to each opponent._
or
**Rings of Brighthearth**
_Whenever you activate an ability, if it isn't a mana ability, you may pay 2. If you do, copy that ability. You may choose new targets for the copy._
, and you activate an ability or cast a spell that would sacrifice such a permanent, it should not trigger since all casts are paid BEFORE the ability/spell is put on the stack, but on xmage, the trigger happens regardless.

**Heartfire**
_As an additional cost to cast this spell, sacrifice a creature or planeswalker.
Heartfire deals 4 damage to any target._