Managers Derek Adams and Danny Lennon have avoided immediate touchline bans following their bust-up last month.
The pair were sent off after a confrontation during Ross County's 2-1 win over St Mirren at Victoria Park.
Both men have been given two-match penalties by the Scottish FA, suspended until the end of the year.
The suspensions will therefore only come into effect if either man is guilty of breaching disciplinary rule 203 again during that period.
The regulation refers to "misconduct at a match by the adoption of a threatening and aggressive attitude towards an opposing member of team staff".
Buddies boss Lennon was also charged with "repeated use of offensive, insulting and abusive language".
The SFA tribunal ruling on the case also reminded both managers to be mindful of staying within the technical area surrounding the dugout in future.