The community had been shaken but felt "more strongly for those involved".
Tate said he was alerted to the situation while leading a service and told the congregation that everybody would have to leave using another exit.
It was important that the children did not see anything, he said.
"We protected the children."
Incredible rescue efforts had been underway outside as church security staff tried to save the man.
Tate said staff were aided by a member of the public who got out of a car with a fire extinguisher to try help.
People had done their best to help but it had been too late, Tate said.
"You can't prepare for that."
Tate said he held a debriefing afterwards with staff to ensure those involved were offered counselling.
People who were unable to access their cars were offered rides from other church members, he said.
A youth service scheduled for tonight would go ahead, which Tate would be attending along with extra security on the door.
A police spokesperson said members of the public helped to put the fire out, but unfortunately the man died at the scene.
Detective Senior Sergeant Rob Hanna told the Herald this afternoon that police have established the death is not suspicious and will be referred to the Coroner.
Officers said earlier they believed they knew who the man was and he was possibly in his late 50s and appealed to members of the public who saw anything to contact Dunedin police.
The church's main services take place at 10am and 6pm on Sundays.
Nations Church promotes itself as valuing relationships with others.
"At Nations, church means people," their website says.
"Ordinary people radically set free by a life-changing encounter with the Lord Jesus Christ, serving Him with all of their hearts, and sharing that new life with others in the community. Such people are worshippers. They enjoy expressing their love for God in a free and contemporary fashion.
"They also see relationships with others as important. True worshippers love others for who they are not what they do. We, at Nations, are also committed to seeing people reach their full potential as they serve Christ in partnership with others."
WHERE TO GET HELP:
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call police immediately on 111.
OR IF YOU NEED TO TALK TO SOMEONE ELSE:
• LIFELINE: 0800 543 354 (available 24/7)
• SUICIDE CRISIS HELPLINE: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• YOUTHLINE: 0800 376 633
• NEED TO TALK? Free call or text 1737 (available 24/7)
• KIDSLINE: 0800 543 754 (available 24/7)
• WHATSUP: 0800 942 8787 (1pm to 11pm)
• DEPRESSION HELPLINE: 0800 111 757