Atkins is being held on $2 million bail, officials said on Sunday.
On Saturday, Gene Evin Atkins, 28, argued with his grandmother about his girlfriend staying at his grandma's South Los Angeles house.
Ms Egland said that Ms Madison "didn't want the girl over there anymore".
"She was the person I loved the most in the world", Corado said. Mr Atkins' girlfriend was allegedly injured by a bullet as well.
Don Kohles, 91, told CNN he saw the vehicle crash into a fire hydrant or a utility pole in front of the Trader Joe's. During the chase, the suspect fired at officers, shooting out the back window of his auto.
More gunfire ensued before Atkins crashed into a pole outside the supermarket.
A woman was shot and killed when Atkins ran into the Trader Joe's supermarket in Los Angeles' Silver Lake section on Saturday, but no hostages were seriously hurt before the man handcuffed himself and surrendered about three hours later, police said.
People frantically tried to flee from the store and some were seen climbing through windows, jumping down and others darted through the back door.
He ran upstairs, seized a couple of his co-workers with him, and made his way into a storage area. He placed a folding storage ladder outside of a window, helping colleagues escape to safety, he told KNBC-TV.
"I grabbed an emergency ladder, barricaded the hallway, grabbed a weapon, put the ladder out the window and just tried to get the attention of the SWAT officer", Gerace told the television station.
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A Los Angeles supermarket was barricaded after a gunman entered the store and took employees and victims hostage until eventually surrendering himself to the police. Police believe Corado was shot inside the store, possibly during this shootout.
She was initially taken to a hospital in grave condition where she underwent surgery and was later considered critical, Moore said.
"A male suspect. become involved in a family dispute which resulted in him shooting his grandmother and a female at the scene", police Sergeant Barry Montgomery told journalists.
The man shot his grandmother seven times and wounded another woman, who he forced into a vehicle, police said.
Atkins, who has two daughters, bounced between several jobs, including working as a security guard, but had been repeatedly fired, Egland said. He also took his wounded girlfriend with him.
The suspect barricaded himself inside the supermarket with an unknown number of people, but was taken into custody "without incident", according to police.
"He did not seem high on drugs, to me", Westafer said.
Trader Joe's released a statement following the incident. A makeshift memorial of flowers, candles and notes grew on the sidewalk outside of the store on Sunday.
"I regret to inform you that there is one fatality that occurred inside, of a woman", Garcetti said, without identifying the victim. The suspect eventually crashed his vehicle outside of the Trader Joe's supermarket and then ran into the store. Our thoughts are with her family, and our Crew Members and customers who experienced this terrifying and unimaginable ordeal.
On Saturday afternoon, the crisis was a hostage situation in a Trader Joe's store in Los Angeles.