The 60-year-old Briton reportedly pleaded for help shortly before she was murdered in the town of Los Cristianos on Friday.
The Tenerife and Canary Islands website newsinthesun.com reported eyewitnesses as saying that a tearful Ms Mills-Westley feared she was being stalked.
It was claimed she entered an employment centre not far from the shopping centre and a security guard sent the man away.
Minutes later she was killed.
Ms Mills-Westley's family said they were devastated by the news of her death.
Her daughter Sarah said in a statement: "Mum retired a number of years ago and was fully enjoying her retirement travelling between Tenerife and France where she spent time visiting her daughter and grandchildren, and her other daughter in Norfolk.
"She was full of life, generous of heart, would do anything for anyone.
"We now have to find a way of living without her love and light and we would ask at this difficult time for some privacy as we try to come to terms with our loss."
Ms Mills-Westley, who was originally from Norwich, Norfolk, had two daughters and five grandchildren.
After retiring from her job as a road safety officer with Norfolk County Council, she left Britain.
Norfolk County Council issued a statement praising her warm character.
"Jenny was a popular and well respected member of staff, who during her time with Norfolk County Council worked as a road safety officer working with many schools and children to teach cycling safety training and make Norfolk's roads safer," it said.
Bulgarian national Deyan Valentinov D - with Spanish police only providing the first initial of his surname - has been detained on suspicion of killing Ms Mills-Westley.
The 28-year-old is reportedly homeless, has a history of mental health issues and a police record.
According to local newspaper La Opinion, the suspect had received treatment at the psychiatric unit of a local hospital in February after being involved in previous violent incidents.
Spanish media reported that witnesses saw a man enter a Chinese supermarket at the Valdes Shopping Centre and without saying a word, attacked Ms Mills-Westley with a knife and then cut off her head.
He was then said to have carried Ms Mills-Westley's head out of the shop, allegedly saying "God is on earth".
A regional government spokeswoman said the killer is understood to have obtained a knife from inside the store to launch his attack.
Colin Kirby, of tenerifemagazine.com, witnessed the event. He told Sky News: "It was all a bit surreal. I was heading past the commercial centre and saw a group of people by the entrance and a medical guy going in form the health centre.
"I assumed someone had fainted, walked on, and then I could hear screaming and shouting.
"I glanced behind me and a guy was ambling down the street holding what I assumed to be a joke head, by the hair."
Mr Kirby said security guards chased the man, eventually managing to bring him down and restrain him.
"The guy did not seem completely right to me - he was a bit dishevelled, not particularly smart and as he was walking with the head he was muttering. It was a bizarre scene."
Christina Perez, a legal representative at a nearby court, said a group of lawyers saw the man sprinting out of the store, carrying the head.
"They saw the man running out of the supermarket with the head in his hands," she said.
"A security man from the complex ran after him and jumped on to him so he fell, and then he threw the head on to the road."
Ms Perez, 38, said her shocked and frightened colleagues ran indoors for safety and locked themselves in.
A UK Foreign Office spokesman said Ms Mills-Westley's relatives were being helped by consular staff who were also liaising with the Tenerife authorities.
Police are investigating the man's movements leading up to the killing and studying CCTV and witness statements to establish what happened.
Los Cristianos is a bustling tourist town on the southern tip of the island and is home to many British ex-pats.
It mainly attracts older visitors with its artificial beaches and fishing harbour where pleasure cruises and diving excursions depart.DISCLAIMER Text may be subject to copyright.This blog does not claim copyright to any such text. Copyright remains with the original copyright holder