Cameron and his wife, Elena, were at work, and rushed to the Starship hospital, where doctors were working frantically on Jack, who turns 2 next Friday.
When they were allowed to see him, he was in an induced coma and "shoved full of tubes".
"It was pretty devastating," Cameron said.
Jack is now awake and in a stable condition.
But he was deprived of oxygen, and a scan showed brain damage which may be permanent.
The incident is being investigated and Cameron said there were many unanswered questions, but he wanted only one thing.
"I just want to see Jack recovered and home."
Elena was at the hospital day and night with Jack and was "broken up".
She and Cameron had had to take time off work and were struggling financially as a result.
Ms Kelly had cared for Jack for about three months and for Michael since he was a baby.
She broke down in tears as she spoke about the incident yesterday.
"I love that little boy ... I've visited [the family at the hospital]. We've cried together, we've talked together."
Ms Kelly said she was still caring for children daily, but was too upset to speak further and directed the Herald to her Facebook post.
"I am still struggling to come to terms with the situation ..." it said.
"After a lot of self-doubt and questioning, I have come to the conclusion that what I did during this tragedy was exactly what I was supposed to do and I couldn't have done anything better."
Jemma's and the Ministry of Business, Innovation and Employment are investigating.
Jemma's general manager, Chris Baker, said the company was confident the caregiver responded "appropriately and professionally".
If a child is choking
Back blows: Bend the child forward and give a sharp blow with the heel of the hand between the shoulder blades. Check if blockage has cleared before each blow. If the blockage hasn't cleared after five blows, try:
Chest thrusts: Place one hand in the middle of the child's back and the other in the centre of the chest. Using the heel of the hand on the chest, perform five chest thrusts (like CPR compressions but slower and sharper). Check between each thrust to see if blockage clears.
Call 111 If the child is still choking, continue with five back blows then five chest thrusts until help arrives. Start CPR if the child becomes unconscious.
Source: St John Ambulance