This is a bit difficult to say for certain, because the Puritans, historically, ceased to exist as a distinct cultural group well before the time period that the story is set in. However, American folklore continues to blur the time periods and distinctions between Pilgrims, Puritans, and other colonists of the New England region, and so this question might simply be interpreted as referring to that conglomerate.
The author doesn't seem to take any distinct tone toward these people; most of the story is concerned with Tom and the Devil, and Tom probably cannot be considered a good representative of the average person. There are occasional mentions made of the colonist's past, in that they made war on the local Native Americans, and some attention is given to their superstitions and folklore, although it is unclear if this is meant to be taken as a normal aspect of the culture or the sign of an uneducated and fearful people.
Some attention is devoted to the people of Boston, although mostly from the perspective of Tom's business dealings and social interactions with them. They are mostly made to seem a vulnerable lot; Tom is able to take advantage of a great number of them who are in "desperate need", and the churchgoing types are depicted as generally humble and somewhat plodding in the zeal of their faith. The conclusion of the story refers to them as the "good people of Boston", so overall I think the most charitable interpretation of the author's tone is that it is one of pleasant indifference.