Los Angeles, California (CNN) -- A group of 13 Salvadoran immigrants missing in southern California amid fears that they planned a cult-like mass suicide have been found alive, unhurt and upset to find they were the subjects of an extensive search.

Authorities had been scouring the Palmdale area of northern Los Angeles County on horseback and by helicopter Sunday in search of the group, which included eight children between the ages of 3 and 17, said Steve Whitmore, a spokesman for the Los Angeles County Sheriff's Department. A resident spotted one of the vehicles identified in the lookout at a park and notified the sheriff's department, he said.

One woman in the group told CNN they were "perfectly OK" and were shocked and angry to learn that such an extensive search was under way. The woman, who would not give her name, said they had been praying all night in the park, that they had done this routinely and that their husbands were aware of the practice.

The search began Saturday afternoon, when the husbands of two women in the group reported them missing, the Sheriff's Department said. One of the men said their wives were part of a "cult-like group" and had been "brainwashed" by its leader, and Whitmore said the wife left a purse with her husband and asked her "to pray over" it.

When the husband opened the purse, he found money, mobile phones and notes that "talked about meeting Jesus, talked about deceased relatives soon to meet up," Whitmore told CNN earlier Sunday. That raised concerns that the group members planned to take their own lives, he said.

The husbands told investigators that the group had broken away from a Christian church in the Los Angeles area "and formed a separate group that included both traditional and non-traditional practices and beliefs," the Sheriff's Department said Saturday. Its leader, whom investigators identified as Reyna Marisol Chicas, had taken her followers on a similar outing six months ago "in the apparent belief that there was going to be a major earthquake."

Several members of the group spoke with investigators, and Chicas was held for questioning after giving deputies a false name, Whitmore said. Though no crime had been committed and the group appeared to be praying for 'honest and well-meaning things," he said deputies had to investigate once their husbands filed missing persons reports.

"The letters themselves could be interpreted in many ways," Whitmore said. "Now, some of the language in it could be interpreted as saying goodbye as relatives, but that's an interpretation." But given the husbands' concerns, "It is better to overreact than underreact," he said.

CNN Correspondent Thelma Gutierrez contributed to this report.