Mr Milligan claimed he grabbed his supervisor by the scruff of his shirt.
Later that morning Mr Milligan said he was asked to attend a meeting with the Freight Lines chief executive, where he was told to leave Freight Lines' premises and not return until further notice, the authority said.
Mr Milligan said that the following day he phoned Broadway's managing director Keith Church.
Mr Church died last year and his daughter Jodie Cole gave evidence at the authority's investigation meeting on behalf of her father.
Mr Milligan said Mr Church advised him that Freight Lines had dismissed him from employment, but told him that Broadway would not be dismissing him, the authority said.
However Broadway did not offer Mr Milligan further work and he was not paid after that date, the authority said.
Mr Milligan said he then made several phone calls to Mr Church, and believing he had been dismissed, asked for a letter to prove it. However, no confirmation of dismissal was provided, the authority said.
Mr Milligan's solicitor then sent a letter to Mr Church raising a personal grievance and asking for his employment agreement, correspondence about the dismissal, and a copy of final pay calculations including holiday pay entitlements, the authority said.
Mr Church responded a month later and continued to maintain that Broadway had not terminated Mr Milligan's employment, despite having not offered him further work, the authority said.
The authority determined that Mr Milligan was dismissed, and considered whether it was justified.
Counsel for Broadway, Marisa Brugeyroux a fair and reasonable employer could have found the altercation with the supervisor amounted to serious misconduct.
However Authority member Helen Doyle said Mr Milligan was denied fair process, including an opportunity to explain why the incident occurred and why he should not have been dismissed.
Broadway was ordered to pay Mr Milligan $4000 in compensation, for humiliation, loss of dignity and injury to feelings and $5821 in holiday pay.
Costs were reserved.
When contacted Broadway did not wish to make any comment.
Mr Milligan could not be reached for comment.