Did you complete Ifrit on the same job you're trying to get your Relic on? That's pretty much the only requirement.
Other than that, the quest doesnt update till you've obtained all 3 pieces, so as long as it's in your key items, you're good.
actually it does update for every one you get.
it will say "go get a white hot ember from ifrit" after you do that it will say "obtain a wing gale" or whatever from garuda. the only thing it doesnt say is "get me that 900 allagan item to finish". but if your paying attention to the quest he does tell you to get that.