If Qyburn comes out of shadows and pulls tryion out of my opponents dead pile, can Tryion then trigger his response to Qyburn coming out fo shadows? I'm thinking no, but figured I would find out for sure.

Yes, he can. Wrong subforum, BTW

He can? Doesn't Tyrion have to be in play before a card comes out of the Shadows? In this instance, it seems like Qyburn comes out of the Shadows and then Tyrion comes into play.

Why should he? He's in play at the right moment for his Response to be triggered, which is the only requirement to use it.

I would think that since Qyburn's ability triggers after he comes out of Shadows, putting Tyrion into play, the action window for responding to cards coming out of Shadows is still open, so Tyrion should be able to trigger off of it, even though he wasn't in play when the card actually came out of Shadows.

Correct.

Fatmouse, you're looking at it backwards. Tyrion does not have to be in play when the trigger is created. The trigger has to be available while Tyrion is in play.