Actually there is an error in the Hillel Calender as well
The Julian Calender belived the solar year is 365 1/4 Days
The Hillel Calender calculates the solar year as 365 days 5 hours 55 Mins
The actual Solar year is 365 days 5 hours 48 Mins
You can see this most in Peseach. The Vernal Equonox is March 21, but Tekutfat Nissan is April 4 or 5(The Halachic Start of Spring)
So technically any year that Peseach occurs before April 4 (or 5th in a leap year) it doesnt occur HALACHICALLY in Spring (Although it really is Spring)