Workers had to go through significant safety procedures and checks before they were allowed to operate the front-end loader - known as a bogger in the industry - that Stainton was on when he died.
O'Leary extended his sympathy to Stainton's partner, Ana-Lee Hemopo, and young son.
"We know that Tipiwai has left a son behind. Our staff will be working with the whanau to support them in every way we can.
"The whanau won't go wanting, they won't be forgotten and we will treat his son as our own."
The company will work with the family to see how it can help.
The mine will remain closed until Wednesday while WorkSafe New Zealand and police investigations into the death continue and O'Leary said he would be paying close attention to the findings.
"We also know that with Tip's passing, it can't happen without meaning and we have already begun work to determine how the tragedy happened and to make sure no whanau will ever go through it again."
O'Leary will be speaking on behalf of the company at Stainton's tangi at the Maraenui Marae near Te Kaha today. Many of the company's 300 staff members are expected to attend. Stainton's body is understood to have been taken to the marae on Saturday.
The mine has been closed since Stainton lost communication with his team about 6.30pm on Thursday after his machine rolled.
It will reopen on Wednesday after a blessing.