My iCaldendar time zone won't update in iCloud?

I was using my calendar in iCloud (via Google Chrome) and setting up a bunch of appointments, then when I looked at it on my iPhone, all the times were wrong. It turns out that in iCloud it was set to Los Angeles times instead of New Zealand time. I updated the time zone in my iCloud settings and turned on time zone support in the calendar, but a day later the time zone is still incorrect in the calendar?

How can I make this update?

My calendar on my iPhone is showing correctly now (I updated all the appointments to the correct time zone), but when I look at it through iCloud online it's all showing in LA time still (despite my iCloud settings showing as NZ time).