I shudder to think what it must have been like in the path of Cyclone Winston. It is hard to conceive of winds 230 km/h sustained for minutes at a time. I remember vividly what is now known as the Great Storm of 1987 (an extra-tropical cyclone) which pulverised south-east England on 15/16 October 1987. There were (according to Wikipedia – ahem!) gusts close to 200 km/h recorded in Sussex (where I lived), but there were possibly higher ones than these – the anemometers failed. I spent the night listening to trees falling one by one around our house. Opposite the house was (and still is) a very tall Wellingtonia – one of the earliest specimens of this tree planted in the UK – and if that had fallen on us there wouldn't have been much house left. It stood firm, thankfully. That is frightening stuff. But that's probably small fry compared to what Cyclone Winston did.
One thing that I didn't personally experience in 1987 was the storm surge. (Being about 40 km inland kind of protected us from that.) Storm surges are a major cause of deaths in cyclones. The sea level can rise substantially during a storm – and coupling that with a high tide can lead to widespread and sudden flooding.
There are lots of ways that a storm can raise water level. Winds can blow water towards the shore, and the Coriolis force acting on moving water can cause a build up. One simple effect is that the low-pressure in the storm simply 'sucks' the water level upwards.
Atmospheric pressure (about 1000 millibars or about 100 kPa) can hold up about ten metres of water. If you had a thin tube, filled it with water, sealed one end, put the other open end in a bucket of water, and lifted the closed end ten metres into the air, you'd see that you got to the point where the water in the tube couldn't be supported any more. A vacuum would form above this height. See it here! In fact, what you have is a barometer – the height of the water is proportional to the atmospheric pressure. A 1 millibar change in pressure corresponds to about a 10 mm of water. With Cyclone Winston, the pressure dropped to 915 millibar, meaning about an 85 cm increase in the height of the ocean to this effect alone. This may not sound much but the disturbance doesn't remain localized – it will propagate out in a similar way to a tsunami. A fairly small shift in sea level in the ocean can correspond to a much more considerable shift when the wave slows down close to the shore. Throw in the effects of wind and rainfall and so forth, and one can end up with a devastating and sudden increase in sea level.
At a more gentle level, atmospheric pressure is what holds up the water in a pet water dispenser, like the one we use with our chickens. There would be no point having a dispenser more than 10 metres high (that would water a lot of chooks indeed) – there would be no water supported above this height.