No - its their 1st year, not aged 1. The age of a child technically when born is 0 years 0 days at their birth. 1 day later they are 0 years 1 day old. When they reach 1 year they are 1 year xx days old and referred to a 1 year old.
Dates though had no 0th year. Or calendar has no 0th year. So the 2nd day in our calendar is Jan 2nd year 1. Thus why its 1 -> 10,100,1000
Its the media and advertising that loves to jump the gun and get in 2 years of advertising&sales for the one event.
Trivia, in the space race, the deadline for the moon landings was the end of the decade and having lived through that time and old enough to know, they had one extra year up their sleeve, 1970 since that was the last year of that decade.
It is the media and advertising that has hoodwinked us in the last 30 years to believe otherwise. They pulled the same stunt in 1999 and made the USA and many other countries buy up big on stuff for the end of century/millennium in 1999. News papers had to print retractions (in tiny print), and the real celebrations occurred at the end of the decade, century, millennium 2000->2001
But hey if fellow Aussies, and others in the world want to work on modern pop culture and advertisers then who am I to stop them. Go for it.