When Tony snapped his fingers, he saw Natasha
As it says on the tin, much like how when Thanos snapped his fingers he saw Gamora, Tony very much sees Natasha. Whoever snaps sees the person who traded their life for the soul stone (so Bruce could’ve seen her too). I like to imagine that their interaction went like this - a loose parallel of Thanos and Gamora’s exchange:
Tony appears in the soul world through a blinding flash of white light, he turns slowly and observes his surroundings. Then, there, in the distance, a woman standing in front of a large building. Much like how Gamora was framed by a structure in her home world, Tony eventually realizes that the woman is Natasha, gazing longingly at the outer facade of the Avengers Compound.
“Nat?” He asks as he walks towards her, and then she turns to look at him, her actions slow and steady. When Nat sees who it is, her expression turns soft, sad, but her eyes are full of fondness and love.
“Did we do it?” She asks.
In that instance, Nat looks happy, so very, very happy. Then it fades as she appears to realize what Tony’s appearance means. She gets a pained look in her eyes, accompanied by a soft, sad smile as she reaches forward and takes Tony’s hand.
“Tony,” she murmurs, a look of love and a soft, sad smile on her face. He clasps his hands around hers tighter.
“No one else was supposed to die,” Nat whispers at last.
An identical look of pain and love cross Tony’s face, a sad smile mirroring hers. Then a flash of white light, and he’s back on Earth for the last few minutes he has left.