Hearts and Hibs have been fined £6,000 and £6,400 respectively while Rocky Bushiri has been handed a two-game ban after it all kick-off on the last day of the season.
Hibs were hit with the higher penalty due to a previous breach of the same rule last year. Staff and players from both sides piled onto the park to confront each other after the 1-1 draw at Tynecastle, which saw Hearts pip their rivals to fourth spot in the Premiership after playing an hour with ten men.
Youtaro Oda opened the scoring early before Kevin Nisbet took advantage of Alex Cochrane's red card, firing the resulting free-kick beyond Zander Clark to level things up.
Tempers flared after the final whistle however, after Lee Johnson appeared to aim a dig into the ribs of opposite number Steven Naismith after they shook hands.