But when the sun is on the bottom half of antarctica, wouldn't the entire northern hemisphere (and most of the south except antarctica) be in darkness?
Sure, but only for six hours.
So the entire northern hemisphere would be in darkness for 6 hours every day in Winter at the same time?
Also, for the first bit after the equinox (when the N. Hemisphere is experiencing autumn), when the sun is "below" antarctica, the very top portion of the
north polenorthern polar region would have to be receiving sunlight, whereas the bottom portion (the part closer to the sun) would be receiving none.