Fonseca had reportedly designated another former Chelsea star Christian Pulisic to take the Italian giants' penalties.
The Italian giants had been awarded a first half penalty against Fiorentina on Sunday, which was taken and missed by Theo Hernandez.
Gazzetta dello Sport reported Fonesca had been unable to give the message for Pulisic to take the spot-kick.
The American reportedly 'respected' Hernandez experience at the club, as he allowed the Frenchman to take up and take the penalty.
AC Milan boss Paulo Fonseca was reportedly angered to AC Milan stars ignored his orders
Fonseca reportedly stressed at half-time that Pulisic was the club's penalty taker, with the American expected to step up to the spot when AC Milan were awarded a second spot-kick in the second half.
Tomori was then seen handing the ball to Abraham, rather than Pulisic, with the former Chelsea striker facing Fiorentina goalkeeper David de Gea.
De Gea ultimately denied Abraham from the spot, with the Spaniard preserving Fiorentina's 1-0 lead.
Pulisic levelled the score on the hour mark, but AC Milan again fell behind with Albert Gudmundsson scoring the winner for Fiorentina in the 73rd minute.
A difficult afternoon for AC Milan was compounded when Hernandez was sent off in second half stoppage time.
Fonseca reportedly reacted angrily to Tomori and Abraham defying his half-time instructions, with the duo now said to be at risk of being dropped to the bench for AC Milan's next fixture.
Pulisic had scored from the spot last month against Venezia, with the American boasting a faultless record of 10 consecutive successful penalties during his professional career.
The defeat leaves AC Milan lying sixth in Serie A after seven matches heading into the international break.
The Italian giants could have moved level with defending champions and arch rivals Inter Milan in second had they beaten Fiorentina.
It is not the first penalty argument to leave a manager raging in recent years, with Chelsea players involved in farcical scenes in the Premier League last season.
Cole Palmer took and scored a penalty in the Blues 6-0 win over Everton, only after forwards Noni Madueke and Nicolas Jackson had to be separated following an on pitch argument.
Conor Gallagher and Malo Gusto had broken the pair up, with then Chelsea boss Mauricio Pochettino slamming the incident post-match.