Corey Lewis first noticed the woman as he crossed the Walmart parking lot in Marietta, Ga., on Sunday afternoon. She was sitting in a Kia sedan, he said, as he led the two children he was babysitting back to his car.

By the time he had them buckled up and ready to go, he had his phone out and was live-streaming on Facebook as he narrated a story about how the strange woman had begun stalking them after he refused to let her talk to the children, Mr. Lewis, 27, said in an interview.

She followed him out of the parking lot, to the gas station across the street, and to his home, where Mr. Lewis, who is black, was questioned by a Cobb County police officer about why he had with him two young children, who are white.

“I didn’t know what was going on, what she wanted to do,” Mr. Lewis said on Tuesday, believing that the woman had called the police because he was a black man walking around with two white children. “I felt like my character was being criminalized.”