How does Agatha, even while in the water and hooked into the Precrime computers, make a choice?

I don't think Agatha makes a decision. With the other two Precogs, she projects visions of crimes that have yet to happen to the PreCrime Division. Agatha is the most talented of the three Precogs, as Iris Hineman tells John when he visits her greenhouse. Her mother is Anne Lively, a mysterious murder case that John investigates.

Throughout the film, Agatha endures immense psychological pain, forced to witness bleak and traumatizing events over and over again. Even so, she is able to bring peace to John and his wife, Lara, when she tells a beautiful story about who their son would have been had he lived, which gives them closure on the event.