This list seems to be mixing standard time and daylight savings time.
Loosely speaking, Northern Hemisphere locations are in "standard time" and Southern Hemisphere locations are in "daylight time". Right now it's the middle of Winter in New Zealand, so selecting "+13" is very weird.
There are some exceptions though, Europe/Dublin and America/Grand_Turk are showing DST
rather than standard time.
Southern Hemisphere in DST:
Pacific/Auckland is +12, +13 DST, listed here as +13.
Australia/Sydney is +10, +11 DST, listed here as +11
Northern Hemisphere in standard time:
Europe/London is +0, +1 DST, listed here as +0
Europe/Athens is +2, +3 DST, listed here as +2
America/Chicago is -6, -5, listed here as -6
But some Northern Hemisphere locations are DST.
America/Grand_Turk is -5, -4 DST, listed here as -4
Europe/Dublin is +1, +0 DST, listed here as +0
There are probably more. I found these manually.
IMHO everything should be listed in STD time.