Counsel for the 34 families, advocate Dumisa Ntsebeza, was cross-examining Association of Mineworkers and Construction Union (Amcu) president Joseph Mathunjwa.
Ntsebeza told Mathunjwa that the "families are keen to know how their relatives met their deaths" on August 16.
"I want to satisfy myself and assist the commission in getting your position, because the families have heard your role in not assisting the situation on August 16," he said.
"We, as the families, hold SAPS and Lonmin to be responsible for the deaths."
Ntsebeza said it was evident there was animosity between Amcu and the National Union of Mineworkers (NUM) in the build up to August 16.
"At the end of this inquiry, I will submit that in the days leading to August 16, it appears there was no love lost between NUM and Amcu.
"Between the leadership of the two unions, you do not see eye to eye. Is that a fair submission?" he asked.
Mathunjwa responded: "Not in person, but [we differ] on issues."
Ntsebeza said that of the 34 people who died on August 16, 10 were members of the NUM, 17 of Amcu and seven were "un-unionised".
Ntsebeza read an article narrating how Mathunjwa was expelled from the NUM in 1999 after he refused to attend an internal disciplinary hearing chaired by the ANC's now secretary-general Gwede Mantashe in Douglas.
But he said he had not received any communication of his expulsion from the NUM other than that no deduction of union fees was reflected on his payslip.
The three-member commission, chaired by retired judge Ian Farlam, is probing the deaths of 44 people in strike-related violence at Lonmin's platinum mine in Marikana, North West.
The dead include 34 people shot dead by the police, who opened fire while trying to disperse a group of strikers gathered on a hill near the mine on August 16.
In the preceding week, 10 people, among them two police officers and two security guards, were hacked to death near the mine.
President Jacob Zuma announced the commission in August. Zuma said it would compete its work within four months, and would have to submit its final report a month later. – Sapa