"Oh my God," Webster said as the cat emerged from under a pile of debris. "Come here, kitty. … You've got to come up here, baby."
Webster said her brother, Troy Kremlacek, lived in the house with his wife and child. The couple, wed in May, also operated a day care in the house. The two adults were with their child and four other children in the house when the twisters hit Monday.
She said that Kremlacek's wife and the children had been released from the hospital but that her brother had stayed overnight because of abrasions he'd suffered on his back. She said Kremlacek and his wife had used their bodies to protect the children.
"The kids were just troopers," she told ABC News. "They had to have God watching over them. … They were so good. It's just unbelievable."
Though Webster said she could not remember the cat's name, she said it had been called "Miracle" at one point. The family also had two dogs that survived and several other cats.
"All [my sister-in-law] could do is [say] 'Get my cats! Get my cats!'" Webster said as she coaxed the cat to her. "[She's] gonna love you!"
ABC News' Bazi Kanani and Jim Scholz contributed to this story.