One of the organisers, retired Archdeacon Robin Kingston of the Holy Trinity Anglican Church, confirmed that the families had raised their concerns at the Thursday meeting.
But he was confident that the service, which is timed to finish at 3.44pm - exactly 12 months after the mine exploded - will now be "non-political."
Mr Kingston said: "The families are keen to ensure that this is a service that deals with their grief and with the community's grief.
"They are trying to get their heads around the fact that so many people have actually asked to come.
"The meeting last night was our normal meeting to plan the final details of the event but the families wanted to ensure it was not a political event. We have been working with the families to ensure that we get it appropriately right, and that is what we have done. "The emotions are pretty tender and little things can really hurt, and we're doing our best to try and ensure that doesn't happen."
He confirmed that the Governor General and the Prime Minister had "agreed to swap roles" to ensure that "the whole service remained non-political".
He added: "The Prime Minister will do a reading, and the Governor General will do a speech. No politicians will speak at the service at all, and that is very significant."
Grey District Mayor Tony Kokshoorn, who lost a number of friends in the mine, was also "in no doubt" that the families wishes had been met.
He said: "There were concerns raised during the week, but it's now totally under control.
"I'm in no doubt that politics won't come into it tomorrow. I know the politicians are all going to great lengths to make sure that doesn't happen.
"The only request for attendance has come from the three local MPs who have all had their leaders requesting attendance at it, and we are accommodating John Key, Phil Goff and Russell Norman, and no one else has asked to attend.
"The three local MPS themselves will be part of the crowd.
"It will be a day of remembering 29 men who lost their lives a year ago and helping their families grieve and move through it."
A number of memorials will be held tomorrow, including a strictly private service for the families in the morning at Atarau, near the mine entrance.
They will also open a 29-rose memorial garden in Greymouth and attend another memorial service in Blackball.
The main event at Rugby Park is expected to attract more than 3000 people.
It will feature an address from Engineering, Printing and Manufacturing Union delegate Jed O'Connell on behalf of the 29 victims, Mr Kokshoorn on behalf of the community, Bernie Monk for the families, and Focus Trust family liaison officer Kathryn Leafe.
Alisha Osborne, 14, whose father Milton Osborne died in the explosion, will sing.
Tracey Cameron will also perform a tribute, to her stepson Ben Rockhouse who also perished.
Portable stages were being set up this afternoon, along with giant TV screens.
The service will begin at 2.45pm and finish after observing a minute's silence at 3.44pm.
