The millenium parties were all on New Year's Eve of 2000, not New Year's Eve of 2001. Some nerds had to be worrying about Y2K date/time bugs instead of partying too.
It was the eve of the new year, the evening that started at the end of 1999-12-31 and ended in time for brunch on 2000-01-01. I was partying with the fun people after arguing the numbers for a few days in 1998 or 1999.