The Matangi Tonga reported that Mr Fungavaka and a relative were arrested on the night of August 17, in the Nuku'alofa CBD, for public drunkenness.
Crown prosecutor Sione Sisifa told the court two police officers, constables Fatai Faletau and Salesi Maile, led Mr Fungavaka to a nearby police station on foot.
It is alleged one of the officers hit Mr Fungavaka on the head with a torch - causing him to collapse.
Later it is alleged Inspector Kelepi Hala'ufia again hit Mr Fungavaka on the head with a torch, before all five officers - including constables Manu Tu'ivai and Tevita Vakalahi - allegedly beat him repeatedly; punching him in the face and body and with at least one officer stomping on his head with heavy boots.
Mr Fungavaka suffered a further beating when he was put in a cell with civilian Semisi Kalisitiane Manu.
The New Zealand police officer was not taken to hospital until 6am the next day. Mr Fungavaka's head injuries were so serious he needed surgery, from which he never regained consciousness.
All six accused, who have been on bail since September, face alternative charges of causing grievous bodily harm.
Earlier in the day the inquiry was delayed because of concerns evidence from four defendants with the same lawyer would clash.
Charges were laid against five police officers and a fellow detainee after New Zealander Kali Fungavaka suffered fatal injuries in a Tongan police cell on August 17 last year.
Mr Fungavaka's family - including his wife Audra Watts, younger brother Bishop and mother Rosemary - travelled from New Zealand for a preliminary inquiry in Nuku'alofa Magistrates Court yesterday.
But the hearing was adjourned earlier in the day after the lawyer for four of the defendants, Mele Kioa, told the packed court the evidence of her clients would clash, Matangi Tonga reported.
Ms Kioa said the evidence of civilian Semisi Kalisitiane Manu, who was also in police custody at the time of Mr Fungavaka's death, would contradict that of accused police constables Fatai Faletau, Salesi Maile and Manu Tu'ivai. The hearing was adjourned so they could find separate legal representation.
Two other accused police officers - Inspector Kelepi Hala'ufia - who was supervising officer on the night of Mr Fungavaka's death, and constable Tevita Vakalahi are represented by their own lawyers.