the moon - strange moonset around 10 pm (3.2 2014, NZ) - explanation?

during a visit to New Zealand we observed (on 3.2 2014) a strange moonset in Te Anau.

Around 10 pm, shortly after sunset, the moon appeared, but then quickly began to go down, and about 1 hour or less it "touched" the mountains on horizon and shortly after it completely disappeared and then we did not see it anymore.

I did not bring a camera or camcorder, so I only have this bad photo from a mobile phone:

The whole process was pretty fast, so I only have one picture. I've never seen anything like it - usually (in Europe) the moon comes out after sunset rather than going down :-)

There was also one guy living there more than 10 years, but he was apparently surprised too.

Can anybody explain this? Is it something normal in this location?

thanks