What does Putnam say that terrifies Tituba and causes her to say that she told the devil she did not want to work for him?
She should be hanged and so she shifts the focus from herself by denouncing that she wants to work for the Devil.
Tituba confesses because Abigail basically puts her in a corner and blames her for the entire evil practice performed in the woods. She confesses more in depth to her association with the Devil once she is threatened by her master, Reverend Parris, with being whipped to death, and by Putnam, who said that she should be hanged.
Hale skillfully starts off by intimidating Tituba, demanding that she confess to a pact with the Devil. He forces questions and causes her to lie to save herself and prevent another beating. She's persuaded to "name names". Once she gives him what he wants, she's treated well, this persuades the girls to lie too.
After being beaten and pressured to confess, Tituba confesses that she was in a pact with the Devil. As a slave, Tituba was aware of how powerless she was and decided to just tell them what they seemed to want to hear and her torment. She also goes further and indict several other women as being in league with Satan as well.
Tituba confesses to witchcraft since Abigail and the others were claiming she had committed the crime. Tituba was wanting to escape the extreme punishment of whippings and being hanged and so she took the easy road out and just confessed to a crime she had not commited. The punishment was lesser and she was allowed to just go to church to get the devil out of her instead of getting killed for "witchcraft".
Tituba was one of the first to be accused of practicing witchcraft during the Salem witch trials which took place in 1692. Tituba first denied all accusations, but later went all-in and confessed making a pact with the devil. Shen then turned the accusations toward other women in the town, making up things and vowing in features of voodoo and so on, basicly creating the chaos which turned into the Salem with trials. When facing…
I'm guessing you mean Tituba from the Crucible. She acts the way she does at first because she is a loyal servant to the Parris family but then has a change of heart and does not want to be put to death. So she acts in fear of being put to death and that is why she lies and "turns to God" and then blames other people of being controlled by the devil.