World number three Robertson entered the tournament in good form after reaching the semi-finals of the German Masters last week, but failed to carry his momentum into the first-round tie with Jak Jones as he lost 5-1.
Robertson started well with a break of 46, but a missed red handed the initiative to Jones, who went on to open up a 2-0 lead.
A break of 88 helped Robertson fight back briefly to win the third frame, but Jones took control afterwards, triumphing in the next three to ease into the second round.
The match in Hong Kong took place only three and a half days after Robertson’s 6-1 defeat by Shaun Murphy in Berlin, with the Australian cutting a frustrated figure throughout.
Former World Championship finalist Jones will play Zhou Yuelong in the second round on Thursday.
German Masters winner Trump was beaten by Yuan Sijun, who knocked in a 103 in the first frame as he went 2-0 up.
Trump took the third and fifth frames but Yuan stood firm to secure a 5-2 victory and a match against Ali Carter, who beat Allen 5-4.
Higgins beat world champion Zhao Xintong on the way to the Masters final last month but, this time, was beaten 5-3 by the Chinese player, who set up a match against Mark Selby.
Murphy lost 5-1 to China’s Pang Junxu, who made breaks of 134 and 130 on the way to victory.
Overall, nine Chinese players have reached the last 16, a record for any ranking event.