In "Contents of a Dead Man's Pocket", how does the introduction of a second setting increase the suspense?
You have correctly identified that there are two central settings to this terrifying short story (at least for those who suffer from vertigo) - the safe interior of Tom's apartment where he has nothing else to worry about except work and his guilt at leaving his wife to go to the cinema by herself, and then the incredibly dangerous setting of outside the apartment, where literally placing one foot wrong will have disastrous consequences.
The way that suspense is greatly increased in this second setting, as you put it, is through the infinite care that Tom takes in going out of the window and how this is described:
He swung a leg over the sill, then felt for and found the ledge a yard below the window with his foot. Gripping the bottom of the window frame very tightly and carefully, he slowly ducked his head under it, feeling on his face the sudden change from the warm air of the room to the chill outside. With infinite care he brought out his other leg, his mind concentrating on what he was doing. Then he slowly stood erect....
Note how this description marks a complete change in the story. We see a man having to move very slowly, plan his every move and enact it with great skill and care - for he knows the cost if he should fall.
I assume that you mean that the first setting is the interior of Tom's apartment. In that case, we are introduced to a second setting when Tom goes out on to the ledge of the building. When Tom goes out there, the story becomes much more suspenseful.
The reason for that is pretty clear. In the first setting, there is no tension. All Tom does is hang out for a bit while his wife gets ready and goes off to the movies. But then the second setting comes in and all of a sudden Tom's life is in danger. That is clearly a whole bunch more suspenseful than some guy in his apartment waiting for his wife to get ready and go.