Tegan works as director of communications for Kyle's King Kyle company, and has been rumoured to be in a relationship with the shock jock for a number of months.
Kyle broke the news of his split with ex-girlfriend Imogen Anthony after eight years together on his radio show last month: "It ran its course and we haven't lived together for some time. We split several months ago."
A passerby who observed the incident between Kyle and Tegan, who did not wish to be named, told Daily Mail Australia he was walking to work on the other side of the road when he saw the pair shouting at each other close to the Beach Road Hotel.
"She was shouting at him 'get me bag, get me bag' and he replied with something like 'I'm calling police and they can get the bag'," the onlooker told the publication.
After going to the passenger door to retrieve her bag, the source said Tegan tried to seek refuge with bin men who were working in the area.