The sister of one victim commented on social media that "this never would have happened" if the victims had prioritized lives over productivity.
According to the company, its team "worked quickly” in response to the tornado.
As the storm swept through the warehouse on Friday, the roof collapsed.
Amazon spokesperson Kelly Nantel stated in a statement that the company was "deeply saddened" about the deaths.
Clayton Cope (29), one of the victims, spoke with his family via phone just before the Edwardsville, Illinois building was destroyed.
Clayton's mother Carla said that Clayton had called her to warn him about the approaching tornado.
Carla said that she told Carla that it appeared that the storm was headed that direction and that he should seek shelter.
Clayton, who was a Navy veteran, said to his mother that he would warn his coworkers.
According to Amazon, the tornado warnings for Edwardsville were issued between 20:06 (local time) and 20:16 GMT (01:06 GMT and 01:16 GMT). The tornado hit the building at 20.27.
According to the company, the team worked quickly to get as many partners and employees to the "shelter-in-place" site.
Austin J McEwen (26), a cargo driver, died in the bathroom. Many workers claimed that they were directed to shelter by emergency alerts received on their mobile phones.
"I was just getting into the building when they started shouting, Shelter in place!" David Kosiak (26), who has been working at the facility for three month, said that he was happy to help. "We were in bathrooms. They sent us there.
"It was like a train passing through the building. Ceiling tiles flew down. It was quite loud. They gave us shelter until we left, which took at most two-and-a half hours," Mr Kosiak stated.
Amazon stated that employees should be notified of a tornado warning and directed to evacuate to a designated shelter in place.
While the majority of the team took shelter at the "primary designated location", a few others sought shelter in an area of the building that was damaged by the tornado. Amazon stated that this is the area where the most tragic loss of lives occurred.
However, Clayton's sister Rachel said to the BBC that she understood from the conversation with her parents that Clayton and the other workers weren't immediately given shelter after the sirens sounded.
She left a comment on Facebook asking for media attention about the company's safety and health policies.
She wrote, "Everyone knows that Amazon cares only about productivity."
She stated that she was unsure if her brother would have died if the company had "got them [the workers] to safety after it got bad and took it seriously".
She wrote that "No one would have been hurrying to get to shelter last minute" and that her brother wouldn't have to go to extremes to help others.
"I want them all to answer this. I want this to be the starting point for places that take the lives of their employees seriously, and treat them as more than just a number.
On Friday evening, deadly storms struck six US states, causing nearly 100 deaths and destroying homes and businesses in an area of 200 miles (322 km). Eight people died in a candle factory in Mayfield, Kentucky.
According to the National Weather Service, the storm intensified quickly as it hit the Amazon warehouse. Winds reached speeds of 150 miles an hour (241 km/h), ripping off the roof from the structure that was about the size of a football field. The concrete walls that were 11 inches thick (28 cm) collapsed on themselves.
Stuart Appelbaum, President of the Retail, Wholesale and Department Store Union, said that it was "inexcusable," that Amazon required employees to work despite a tornado warning.
On Monday, US Department of Labor said an investigation into the building collapse has been opened by the US Occupational Safety and Health Administration.Rebecca Givan, associate professor at Rutgers University's School of Management and Labour Relations, said companies have a legal requirement to maintain a safe workplace but the penalties for violating it are very weak.
She said that ethically, companies should prioritize the health of their employees. If they have to tell customers that delivery might take longer, they should be open to doing so.
She said that Amazon does not employ many of these workers directly, but instead uses subcontractors to avoid questions about whether the workers should have been called in on Friday evening.
Jeff Bezos (the founder of the firm) was also criticised for posting photos of astronauts returning from a space tourism trip on his Blue Origin rocket.
Later, he tweeted "The tragic news from Edwardsville." We are heartbroken by the loss of our team members there. Our thoughts and prayers go out to their families.
Amazon announced that it would donate $1m (PS757,000), to the Edwardsville Community Foundation, and also provide relief supplies such as food and water.
