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I had a similar case happened about two years ago at Ponsonby in Auckland.
I went to a meeting with a colleague and parked in a P30 parking space beside Ponsonby Road. After 25 minutes I popped out of the meeting and moved the car to the space in front of the one I used ( I checked that there was no tyre marking before I sat into the car).
The difference from your case was I did not leave the car immediately, because I was waiting and wishing there could be a space available at the opposite side of the road.
After about two minutes I noticed in the rear mirror that a parking warden was sneaking at the back of my car and writing on his PDA. Then he printed out a long piece of paper and walking towards the front side of the car. However he suddenly turned around, walked away and put the paper in his pocket once he passed half length of the car and realised the driver was sitting inside.
I was quite surprised about the the attitude change of this parking warden- it saved my time of explanation to him anyway.
Unfortunately I received a ticket of $12 by letter for parking 35 minutes in a P30 space. This really pissed me off; nothing about money but matter of principle. From my point of view, parking warden is used to make the society better, not just purely collecting money. As I was still in the car, that parking warden should hand the ticket to me in person and explain to me should move and park a car in the same parking area is not allowed, or the time is not re-calculated in such case. And the most important, I did move the car and the car was physically re-parked before the 30-min expired.
I wrote back to Auckland Transport explained the car was moved and re-pakred. My client and colleague could be my witness of that I left the meeting for moving the car. Also complained that parking warden's behaviour.
Auckland Transport waived the ticked (This means re-park in the same area is allowed and time is re-calculated). However, Auckland Transport "made" a nice story saying that parking warden saw the tyre mark was still there when he was back. That was why he issued the ticket. But as I have said above, there was no tyre mark at all before I moved the car. Absolutely a shame of Auckland Transport.
My suggestion is take extra care- use dashcam when you are on the road, take photo after you park (especially in short term parking zone). Because SHIT HAPPENS.