It is not a mistake. In Florence the new year began March 25.

Up until 1528, not only in Florence but throughout the Christian world, the year began March 25 that is to say the day of the Annunciation, exactly nine months before the birth of Jesus (Christmas). The moment of the incarnation of Jesus in Mary’s womb is on its own a symbol of birth and hope in the future and it also coincides with the arrival of spring. They both were perfect symbols for the start of the new year with the best omens.

In 1528 Pope Gregory XIII introduced the new solar calendar (the one we use now) which is based on the study of celestial bodies and the cycle of seasons. The preceding calendar, the Julian, was instead based on religious festivities  and caused calculation problems over time. The Florentines, however, disagreed to introduce the new calendar. They did not want to give up celebrations in honor of the Madonna, whom they have always been most devoted to.
In fact for this occasion many people come to the city to worship the image of the Annunciation at SS. Annunziata church. The tradition says that her eyes had been painted by the angels. It was the Grand DukeFrancis III of Lorraine to impose the new calendar and so from 1750 also in Florence the year started Jan. 1. The tradition is not entirely lost because on March 25 we still have celebrations. The ancient festival is repeated with a parade that starts from Palazzo Vecchio in order to arrive at the Basilica of the Santissima Annunziata. Happy New Year!