The workers were reportedly protesting the alleged injustice by their employer when they were shot by the officers.
The victims, who were protesting at the company's headquarters in Ajao Estate, Lagos, died from gunshot injuries sustained in the leg and thigh respectively.
One of them, identified as Daniel Osikoya - a 19-year-old; had just joined the company few days before he was killed.
The workers were said to have protested the maltreatment of casual workers by the management. They claimed the management only caters to the welfare of the full-time workers.
The aggrieved workers said they were ignored during the Yuletide as welfare packages were given to full-time employees, so they decided to take some of the company's products, perhaps without the due approval of the management.
"It is pure injustice to give only the full-time workers gifts without giving any to casual workers, who do most of the jobs. That was why we fought for our rights. It is unfair for the policemen to attack us. We were about to move the cartons out of the company's gate when the policemen invited by one of the company's security men started shooting," one of the casual workers told the newspaper.
"Bullets hit Daniel in the thigh and another worker was shot in the leg. I was with the two workers that were shot; it was God that saved me. They shot at us as if we were thieves.
"They were not taken to a hospital on time and Daniel died around 8am that day. He bled to death. The other victim died this afternoon (Tuesday). Because of that incident, we were not allowed to work," the worker said.
Another worker, who claimed to have spent two years in the company, said: "Each worker usually takes away a carton of drink at the end of the year. Some production workers on afternoon duty had already taken some cartons on Friday and our bosses didn’t talk.
"Those on night duty wanted to leave with their own cartons around 5am on Saturday when the policemen started shooting. Two persons died from the injuries they sustained.
"Later, policemen attached to the company came to the gate and told their colleagues to let us go with the products.
"Most members of the management are Indians. They are treating us like slaves in our own country."
Father to one of the diseased, Olufemi Osikoya said the company did not inform the family on time after the shooting.
He said: "My son was a decent person. If not for some issues the family is sorting out, he was supposed to have been in a higher institution.
"He was shot in two places. Instead of them to rush him to a public hospital, he was taken to the company's clinic.
"We were called around 7am. When I got there, he was groaning in pain and had lost much blood.
"He gave up immediately we got to the Lagos State University Teaching Hospital, Ikeja. He joined the company in December. I learnt that his colleague that was shot is also dead."
When contacted, the Police Public Relations Officer in Lagos, SP Dolapo Badmos, said the workers were violent.
She said: "The command received a distress call that workers of Chi Limited were disrupting business activities of the company.
"The command’s operatives were mobilised to the scene to douse tension, but the workers attacked the policemen, throwing caustic soda at them.
"As a result, one inspector suffered severe burns and he is recovering in a hospital. Why should a policeman on duty be attacked? That attitude should stop.
"Attacks on policemen are not right and must be condemned; they are also human beings with families.
"The command received the report that one person was shot dead.
"There is what we call rules of engagement and use of firearms under the police acts and regulations.
"The command has studied the situation and discovered that the personnel deployed acted in accordance with the rules."
The company was not immediately available to comment on the incident.