She was then taken to Auckland City Hospital.
Mr Williams said he called the hospital three times to check on the young woman.
He also spoke to a professor in the group who told him they were waiting to see a doctor.
The professor told him the girl was conscious and lucid and Mr Williams later heard she had left hospital "under her own steam".
Coast Guard duty officer for the northern region Johnny Slough said the girl had mild hypothermia when the Coast Guard picked her up half a kilometre off the shore of Rangitoto.
"She was conscious, [but] she was unable to paddle, which is why the decision was made to bring her to shore quickly," Mr Slough said.
"She was not alert and conscious, she was in a lowered level of consciousness."
Mr Slough said it was thanks to the guide's quick thinking and the immediate availability of a rescue vessel that the situation did not become any more serious.