The elder daughter of the Yau family told local media that her parents tried to defend her sister's boyfriend when the axe-wielding teenager went for him.
"Originally the assailant was attacking my sister's boyfriend and when my mother and father saw, they went up to get in the way and then they got injured," Sylvia, 30, told the Hong Kong-based Apple Daily newspaper Tuesday night.
Both the boyfriend Edmund Au-yeung, 30, and Sylvia's 62-year-old father are in intensive care with serious head injuries, the paper reported.
Her sister Tracy, 26, and mother, 58, were also injured, while Sylvia's 17-year-old brother was unharmed.
The 17-year-old attacker injured a total of five people in the assault on Monday, which was claimed by the Islamic State group.
A video released by the group Tuesday purportedly shows "Mohammed Riyadh" -- knife in hand -- announcing he would carry out an "operation" in Germany, and presenting himself as a "soldier of the caliphate".
Sylvia and her husband, who travelled to Germany on Tuesday night accompanied by officials from Hong Kong's immigration department, told how their family had been enjoying their holiday before the attack.
"My father-in-law's friends received pictures and said they were having lots of fun," said Sylvia's husband, who was not named.
The attack happened at around 9.15 pm on the train between the town of Treuchtlingen and Würzburg in Bavaria, southern Germany.
Witnesses said the carriage looked "like a slaughterhouse", with victims' blood covering the floor.
The teen attacked a woman walking her dog along the river as he tried to flee the train. She is also now fighting for her life.
He was then shot dead by police as he began to attack officers with the axe.