"She actually told them to close their eyes and go to sleep, she was taking them to a better place," he said.
Bystanders and beach rangers went into the water and rescued the children, witnesses and police said. Wilkerson tried to keep rescuers from pulling her children from the minivan and at one point was fighting her son for control of the steering wheel, Johnson said.
Johnson said Wilkerson told investigators she was trying to drive out of the surf, not into it, and has denied trying to harm her children.
Tim Tesseneer was driving along Daytona Beach on Tuesday with his wife when they noticed the minivan driving through shallow water. They heard the screams, he said, of two children, who were crying and waving for help out of one of the rear windows.
Tesseneer threw the car in park and raced over to help. One child was screaming, Tesseneer recalled Wednesday to CNN's Piers Morgan. " 'Please help us, our mom is trying to kill us.' "
The other child he could see was wrestling a woman for the steering wheel. But the woman just kept saying, " 'We're OK. We're OK. We're OK,' " as another man joined Tesseneer trying to get the driver to stop.
With the minivan in the cold, heavy surf of the Atlantic, the second man, Stacy Robinson, opened a door and pulled out the two panicked children. There was a good chance if he and Tesseneer hadn't been there, the children, ages 10 and 9, would have drowned inside the van as it pitched in the water, officials said.
Another child, a 3-year-old girl, was strapped in a car seat. A lifeguard dived in through a front window and unbuckled the child and handed her to another lifeguard as the vehicle bobbed in water about 3 feet deep.
The mother just walked away, Tesseneer said, silent with a strange, almost "possessed" look on her face.
While there is no evidence that drugs or alcohol were involved, Johnson said one goal of charging her was to make sure she gets help for any possible mental issues.
"This is a tragic event. And our goal is to get her into the system so that we can protect the children and take whatever action we need to help her, too," he said.
Wilkerson also is being held on three counts of aggravated child abuse, Johnson said. She has not yet requested an attorney, he said.