When does the Chinese zodiac year start?

It depends on the calendar. By the lunar calendar the new animal starts at Lunar New Year, the new moon that opens the first lunar month, between January 21 and February 20. In saju and BaZi it starts at Ipchun (立春), the start of spring, when the Sun reaches 315 degrees, on February 3, 4 or 5.

It depends on the tradition you follow. Lunar New Year sets the holidays and most popular zodiac charts. Saju, BaZi and the traditional almanacs count the year from Ipchun. Fatescroll reads saju, so it uses Ipchun.

Ipchun is a moment, not a date. The whole world passes it at once, so the local date depends on the clock: when it comes in the morning in Seoul, it is still the evening before in North America. In 2027 it is 10:46 am on February 4 in Seoul and 8:46 pm on February 3 in New York.

Each lunar month starts on the day of the new moon, and Korea's clock runs an hour ahead of China's. When the new moon comes between 11 pm and midnight in Beijing, it is already the next day in Seoul. That happens in 2027: Lunar New Year is February 6 in China and Seollal is February 7 in Korea.

In everyday Japanese use the zodiac animal (eto) changes on January 1. Traditional Japanese fortune-telling, like Four Pillars there, uses risshun (立春), the same start of spring as Ipchun.