Mr Fungavaka, who was in Tonga to bury his grandfather, had been arrested for a minor drunkenness offence after going to a Nuku'alofa club with a relative.
He died after receiving injuries while in police custody.
The officers facing manslaughter charges are Inspector Kelepi Hala'ufia, who was supervising officer on the night of Mr Fungavaka's death, and constables Fatai Faletau, Salesi Maile, Manu Tu'ivai and Tevita Vakalahi.
Semisi Kalisitiane Manu, who was also in police custody at the time of Mr Fungavaka's death, has also been charged with manslaughter.
All six men face alternative charges of causing grievous bodily harm.
They have been on bail since an appearance in September.