This card's effect that makes your opponent take battle damage instead of you is a Quick Effect. (It does not target, and cannot be activated during the Damage Step. Tributing this card is the cost to activate this effect.)[1]
This card's effect that Special Summons it is a Trigger Effect that activates in the GY. (It does not target, and can be activated during the Damage Step.)[1]
Banishing this card that was Special Summoned by its own effect when it leaves the field does not start a Chain. (This effect is also applied during the Damage Step.)[1]
Q&A Rulings
Q: During my opponent's Battle Phase, I activated the effect of "Time Thief Chronocorder". In this situation, which player takes battle damage if my opponent's "Amazoness Swords Woman" attacks directly?