"Notes found in one of the diaries hint that a strong belief that supernatural forces would intervene and save them could have motivated the family to hang themselves."

BBC reports, in "Were occult practices behind India's 'house of mass hangings'?"

The notes in the diaries laid out exactly how the family [of 11] needed to "hang themselves" before they were to be saved. Many of these "instructions" appear to have been carried out... The diaries also said the family needed to cover their eyes and mouths with a cloth during the "ritual". It also specified certain rituals to be performed for seven consecutive days before the "final day". The rituals, it said, would "invoke the spirit" which would ask them to "complete" the task the following day. The notes also said that his mother, Devi, should be "made to go to sleep" in the next room if she "can't stand". It mentioned the time of the "final act" - between midnight and 1am. It also said on that day the "earth would tremble and the sky would shake and it is then that I will come to rescue you".

Police said they are still trying to understand if or why the rest of the family went along with the plans. They believe it is possible that the Chundawat family was suffering from "shared psychotic disorder".... [B]ased on footage from CCTV cameras installed around the neighbourhood, police suspect that the "ritual" mentioned in the notes could have begun on 26 June when one member of the family met a temple priest.

"Temple priest" — what religion are we talking about here? Maybe I missed it, but I don't think any religion is specified. I can see wanting to protect religions from association with this horror, but I don't think facts this significant should be suppressed in a news report.

Here's another report, in The Hindi, with much more detail:

The police said the diaries were dictated by Lalit who believed the “spirit” of his father Bhopal Singh, who died in 2007, was communicating with him and instructing him to perform ‘badh tapasya [banyan tree worship]’ for the betterment of the family....

Lalit, who is at the centre of the macabre tragedy, was a rather complex character...  In 2004, a major incident shook Lalit’s life. “He was pushed under several sheets of plywood and set on fire. We knew who did it but the matter was resolved through a compromise,” said Mr. Dinesh. Lalit lost his voice in the incident.

Things began to change in Lalit’s life in February 2007 after his father died of respiratory illness.... Ms. Sharma said the whole family was devastated and a priest was called for Garuda Purana paath (a prayer) for 10 days after the death.

The religion seems to be Hinduism.

“One of those 10 days, we were all sitting and listening to the prayers when Lalit suddenly started chanting Om. His voice came back and everybody said ‘Daddy aa gaye’ [Daddy has returned],” she said....

Naresh Yadav, who lives a few houses away and was a regular customer at Lalit’s shop, recalled a conversation with him in 2008. “I asked him how he regained his voice and he said his father came in his dream and asked him to perform a puja,” he said....

About that badh tapasya, the banyan tree worship, here's Economic Times:

Police recovered handwritten notes about "attaining salvation", found in two registers, have foxed the investigators who said that they have not seen anything like this earlier. "There is a talk about 'badh tapasya', which indicates that one has to get into a formation like a banyan tree whose branches are hanging. The notes state that by doing this, God would be happy," the officer said.

AND: From One India:

"The notes state that if one follows a set of rituals, their problems would be solved and God would be happy. It seems that the rituals went awry. The notes mention how after climbing the stool and covering one's face and taping the mouth, and wrapping a chunni around one's neck, one has to climb down and help others," an officer privy to the probe said. The notes mention about doing a 'jaap' before starting the rituals and think about 'shunya', so that other thoughts do not cloud their minds....

Police are probing whether the family followed any godman, who might have issued the instructions found in the notes. The notes had stated that "the human body is temporary and one can overcome fear by covering their eyes and mouth." Two members of the family, however, insisted today that even though their family was religious, they did not believe in babas or tantriks and could not have committed suicide....