How vulnerable is New Zealand to tsunamis?
Quite vulnerable. Tsunami hazard for the Pacific is higher than for other oceans because of the "Ring of Fire" - the zone of earthquakes associated with the tectonic plate boundary that bounds the Pacific. In New Zealand, scientists consider the tsunami hazard from two viewpoints - Pacific-wide events for which there will be some warning, and "near-source" tsunami generated by large offshore New Zealand earthquakes, landslides, and volcanic eruptions. The list of possible local tsunami sources is long. Because tsunami research is relatively young (compared to other geological hazards), the state of knowledge about the severity and frequency of local and distant tsunamis is poor. One of the main challenges facing tsunami researchers is that evidence of tsunamis does not stay in the landscape as it is eroded by natural processes. Impacts of past tsunami are therefore difficult to identify, unless someone was around and wrote about them at the time.
Does New Zealand have a tsunami warning system? If so, how does it work?
New Zealand has a warning system for tsunamis caused by distant earthquakes (such as in South America), but does not have a warning system for tsunamis caused by local events. Why? Because tsunami generated by local earthquakes can arrive at the nearest coast before scientists can calculate the location of the earthquake and issue a warning.
As far as tsunamis coming to New Zealand from distant places, the Ministry of Civil Defence and Emergency Management receives warning from the Pacific Tsunami Warning Centre in Hawaii. Ministry of Civil Defence and Emergency Management is responsible for evaluating the danger to New Zealand, and will ensure national or regional warnings are issued, if necessary. Tsunamis from South America, Alaska, and Japan, take more than 12 hours to reach New Zealand, giving authorities time to make decisions.
What should you do in the event of a Tsunami warning?
The sensible (real) answer is simply get to high ground.
However, the apparent answer at this location is simply to stand on one side of a painted line on the road. Obviously it is vital to make sure you are standing on the correct side of the paint, as getting it wrong could make the difference between life and death! As we all know, water has no answer to encountering a painted line in it's path, so in spite of the flatness of the surrounding area you can rest assured that "she'll be right" if you are on the safe side of it.
Yes, I know I am 'Extracting the Michael' on an important subject, but seeing the sign on the road I just couldn't help myself! 
The cache itself should be an easy find. Please message me if you encounter any problems such as a soggy or missing log, or if any marooned shipping is blocking your access!
Any logging which does not match the physical logsheet will be removed, and all feedback (positive or negative) is welcomed in order to help create better caches for the future.