Mark Allen has been fined £250 for swearing during a press conference at last month's UK Championships in York.
A statement from the World Professional Billiards and Snooker Association said that Allen had been fined and "warned as to his future behaviour".
The row between Allen and Hearn has been defused since the left-hander's outburst in York.
Allen's comments had included a call on Hearn to resign.
Judd Trump has also attracted controversy after describing Neil Robertson's play as "slow" and "boring" after their BGC Masters semi-final and insisting he would have beaten the Australian, who beat him and went on to win the title, easily if he had been at his best.
World champion John Higgins has called for Allen and Trump to calm their behaviour.
He said: "It happens. Often when you come off after a big match the adrenaline is still running.
"I'm sure they don't want to keep on getting fined, so it's something they'll definitely learn from.
"Judd doesn't really need to say these things. To say that if he played well he'd have beaten Neil easily, that's being a bit disrespectful to your opponent."