The body of Mr Fallone was discovered in his tent at around 5pm on Sunday, June 30.
Mr Fallone, 64, was one of 25 officers supplied to the festival by security firm G4S.
It is understood he was working night shifts during the five-day event. Police say the death is not being treated as suspicious.
A Justgiving page has been started in memory of Mr Fallone, from Faifley in Clydebank, West Dunbartonshire, to help support his family.
Karen King, who started the page, said: "To say the family are devastated would be an understatement. His family is broken.
"To be going through a loss of a loved one whose untimely passing while in another country takes things to another level.
"This page is to help raise funds to help the family out. Funeral and all the other costs at this time are going to be extortionate.
"Let's help them as best we can as a community."
Coroner Tony Williams said the death of a 64-year-old at Glastonbury Festival had been reported to his office and is being investigated.
No inquest has been opened into his death.
A spokesperson for G4S said: "At 5pm on Sunday, June 30, one of our employees was found dead in his tent at Glastonbury Festival, where he had been working as a security officer.
"The next of kin have been informed and our thoughts are with his loved ones at this difficult time."
A police spokesperson added: "We were made aware of the sudden death of a man in his 60s on one of the campsites at Glastonbury Festival.
"Officers attended and are satisfied the man's death is not suspicious. The coroner has been informed."
Following the announcement of Mr Fallone's death, several people expressed their condolences on Facebook.
Alissa Randall said: "So heartbreaking and sad to read. Rest in peace Sir, my thoughts for his loved ones, friends and colleagues."
Michaela Rose added: "Many thoughts and condolences to the family. Rest in peace X."
David Martin said: "That's sad to hear. My thoughts and prayers go out to all who knew this man."