It is necessary to read into Miller's "a word about Thomas Putnam" early in Act One to understand the dynamics of Putnam and Parris's relationship. Putnam is described as "vindictive" and apparently nursing a grudge because his brother-in-law had been passed over for the post of Salem's minister in favor of George Burroughs. Putnam apparently felt that his wealth and prominence in Salem entitled his family to preferential treatment, and when they didn't receive it, his resentment grew.
In the stage direction in the scene where Ann Putnam is compelled to admit to sending Tituba to conjure the spirits of her dead children, Putnam is described as "intent upon getting Parris, for whom he has only contempt, to move toward the abyss."
Since Parris is relatively new to Salem, he doesn't have a long history with Putnam, but he is a weak personality and frequently bends to Putnam's will. Because Parris is largely unsupported in Salem, Putnam sees Parris as a tool he can use to turn events in directions that will benefit himself; Putnam allies himself with Parris not because of respect or liking for him, but because it is politically and personally expedient.
The history between Putnam and Parris is not told explicitly in the play, although the conversation between them as well as the comments of Giles Corey and John Procter in Act I scene I give us a view of their relationship. Parris is a new minister in a town that has had several ministers in seven years. He has met with much opposition from a sector of the church here as evidenced by Proctor's comments about the nature of his sermons. Putnam has been Parris's supporter in these controversies. He says :"..I have taken your part in all contention here, and I would continue, but I cannot if you hold back in this..."
Historically speaking, Miller is accurate in his portrayal of Putnam and Parris as associates. The Putnams were a major family in Salem and were strong supporters of Parris. Their support of Parris was a part of a social conflict between the Putnams and the Porters who wanted to force Parris out of town. This social conflict was most likely a major cause of the witch hysteria that broke out in Salem.