Here's the wikipedia article (https://en.wikipedia.org/wiki/Vomitorium), vomitorium meant exit in amphitheaters.

Interestingly, this misconception is perpetuated in Hunger Games, in volume 2 Katniss and Peeta attend a party, clearly modeled after the lavish roman banquets mentioned here, at the Presidential Palace in the decadent Capital, which includes a drink to induce vomiting so people can enjoy more food (https://thehungergames.fandom.com/wiki/Food_and_Drink#cite_r...).