I had this come up in a game recently and wanted to check here to see which way was right.

I had fiery kiss in shadows and when I used it, I got Margaery Tyrell (Tales from the Red Keep) out of shadows. Card text:

Fiery Kiss - Response: After fiery kiss comes out of shadows, choose 1 non-army Bara character in your dead pile and put it into play...

Margaery Tyrell - Response: After a card comes out of Shadows, choose a non-Lady character. Until the end of the phase, treat that character as if its printed text box was blank.

The question was would I be able to trigger Margaery's ability? I thought I could since it would be the same response window, but my opponent didn't think that it would. Since I wasn't 100% sure, I just played without triggering it, but I am curious which way is correct.

Yes, you could have triggered her response. It is the same response window. You check play restrictions on responses when you trigger the response - so the card you are triggering does not actually have to be in play when the response opportunity is created.