Juan Jasso was told to "get back to Africa" after tackling the trio for using foul language on the Metrolink tram. Beer was also flicked at him.
Aaron Cauchi, 19, Robert Molloy, 20, and a boy, 16, had been "looking for trouble" when they abused Mr Jasso and two other people on 28 June.
Their abuse of Mr Jasso was filmed by a passenger and was widely viewed.
Joseph O'Connor, prosecuting at Manchester Magistrates' Court, said the racist attack came just five days after the EU referendum.
He said that this resulted in a 41% increase in hate crime, according to government statistics.
Trouble first began about 07:45 BST when a passenger heard "disgusting, vile abuse" on the tram packed with mothers with babies, schoolchildren and commuters, the court heard.
After the trio got off the tram following the confrontation with Mr Jasso, they surrounded Alistair Lambert, "with their chests stuck out and shoulders back, striking him with a cigarette lighter to intimidate him, said Mr O'Connor.
Shortly after, Andrew Guest was cycling to work when he passed the trio and one or more spat in his face and down his body, the court heard.
Cauchi, of no fixed address, was charged with two public order offences and assault over what happened on the tram, and two assaults later in Trafford.
Molloy, of no fixed address, was charged with racially aggravated assault, common assault and using threatening words or behaviour.
The 16-year-old boy, who cannot be named, was charged with using threatening words or behaviour and common assault.
They are due to be sentenced on Tuesday.
Three young males who racially abused a US army veteran on a Manchester tram have admitted going on a "rampage".