There is a mystical quality about Tituba for a variety of reasons. She is from Barbados, and the people of Salem believe that the slave island culture is rooted in a lot of spiritual mysticism. Parris has a good quote that shows audiences that her Christian spirituality is somewhat suspect.
I saw Tituba waving her arms over the fire when I came on you. Why was she doing that? And I heard a screeching and gibberish coming from her mouth. She were swaying like a dumb beast over that fire!
Mrs. Putnam believes that Tituba is the only person in the town that can give her the information that she seeks. Mrs. Putman tells audiences that seven of her children have died. Ruth is now sick, and it looks like she might die too. Mrs. Putnam genuinely believes that her children have been murdered, and she wants to find out who the murderer is. She believes that only her dead children can identify the culprit, so Mrs. Putnam contacts Tituba and asks her to contact her dead children using the Barbados mystical faith.
Mrs. Putnam: And so I thought to send her to your Tituba—
Parris: To Tituba! What may Tituba—?
Mrs. Putnam: Tituba knows how to speak to the dead, Mr. Parris.
Parris: Goody Ann, it is a formidable sin to conjure up the dead!
Mrs. Putnam: I take it on my soul, but who else may surely tell us what person murdered my babies?