The Everton forward had given his side the lead nine minutes into the second half from the penalty spot, only for Anice Badri to pull the home side level just two minutes later.
The drama unfolded shortly after Tunisia's leveller, with Tosun walking leaving the pitch before launching into an animated confrontation with the supporters in the stands behind the team benches.
Reports in Turkey claim that supporters had thrown fireworks, with some hitting the striker's father and other family members who had made the trip to Geneva to take in the match.
While Tosun never entered the stands, with his team-mates and Turkish staff stepping in to make sure he was not in a physical altercation, he was still shown his marching orders for making a throat-slitting gesture towards the crowd.
Tosun apologised for his reaction after the game, saying that he saw his father being threatened, but insisted that his gesture was 'unworthy' of a Turkey captain.
"When I turned my head, I saw a quarrel with my father," Tosun told reporters. "I didn't know the whole story. I told them that they were wrong, threatened, unworthy of me.
"Character is more important than football. It was an unbecoming gesture. I apologise. I guarantee it won't happen again."
Ferjani Sassi put Tunisia on top on 79 minutes, but a Caglar Soyuncu goal in stoppage time earned Turkey a draw on the night, despite playing a half-hour with 10 men.
Tukey have another friendly with World Cup host nation Russia on Tuesday.