Both the mother in "The Umbrella Man" and Norman Gortsby in "Dusk" are intelligent, experienced urbanites who are suspicious of strangers and characteristically alert and watchful. They are both reasonably humane, however, and willing to help someone who is in genuine need. It is just that they have seen too many panhandlers and con artists, and they have made up their minds that they are not going to contribute to idlers or get taken in by grifters. So they are both sophisticated people, probably not too much different from the original readers of the two stories.
They also share one other character trait: they are curious about other people. When the mother sees that the Umbrella Man is not looking for a taxi, she follows him for quite some distance to see what he is actually up to. She does this in spite of the rain and the probable need to get home. Gortsby listens to the young man's story about not being able to find his hotel. When he finds the cake of soap he goes running off to catch young man and to lend him a whole sovereign. Then when he sees the elderly gentleman "poking and peering beneath [the bench]" he wants to know what he is looking for. The reader would never know the full story if he or she were not sharing Gortsby's point of view.