Another question about timing

[StuffedKiwi]

This came up in a game last night.

Teddy hits an Onryo. Candy is standing within 2" of the Onryo.

Teddy triggers 'Peekaboo," "After damaging," tossing the Onryo 4" away and following.

The Onryo's Ability "Persecuted" states that any model within 2" will gain the adversary condition "When this model suffers damage from an enemy model."

Now, my understanding of how timing works is that if two effects occur in the same Step (or both After a Step), triggers go before abilities. So if both the push and the condition are happening at the same time, the push happens first (it's a trigger) and the condition last (it's an ability). Which would be good for Candy, who would not be within 2" of the Onryo after the push, and so wouldn't gain Adversary. But it was unclear to us when the Onryo's ability would come. Are there other models that state something happens "When this model suffers damage"? Does that mean "At the same time as the damage occurs"? Or does it mean the same as "After damaging"?

Any guidance or clarity greatly appreciated, especially if I've misunderstood anything, or there's somewhere I can look that clears this up.

[The Godlyness]

.....after damaging is after damage is applied reduced prevented etc.

When damaging is when all that stuff is being applied. (I.e. critical strike)

So her ability goes off first then she is pushed by teddy.