The brothers were asked to leave by North Star's staff.
Fisher rushed at the victim when he left the premises with his family.
Fisher continued his tirade of racial abuse and obscenities before breaking free and pushing past bar staff, punching the man twice in the face and elbowing him in the head, knocking him to the ground.
The incident was filmed by one of the teenage daughters.
The man was left shaken and suffered bruising and grazes to his forehead.
Rawstorn then attempted to push past staff to get back inside the bar.
Police said the victim then yelled something in Japanese.
Rawstorn believed the man was yelling something derogatory at him and decided to run towards him ''aggressively'', but was restrained by a member of the public.
Fisher and Rawstorn told police the reason for their behaviour was they believed the man was speaking in a derogatory manner about both of them.
Both men were charged with disorderly behaviour and Fisher was charged with common assault.
They entered guilty pleas and were convicted.
They were both remanded on bail and are due to appear in the Oamaru District Court on April 26 for sentencing.