This is a very good question, because it touches on the point where two systems overlap: the Chinese solar and lunar calendars, both of which are used in different stems & branches calculators and tables.
Dr van Buren used the lunar calendar, where the change of the year occurs at the second new moon after the winter solstice — the Chinese New Year.
So for the date 9 February 1980, the year pillar is indeed Ji Wei when using the lunar transition. However, when calculating the day pillar, the usual method follows the continuous calendar count and the numerical key assigned to the civil year used in that table.
In practice, for 9 Feb 1980, when using the standard day-calculation tables, you would normally use the number for 1980 (9), not the number for 1979 (4).
The reason is that the day sequence does not reset at Chinese New Year. Days move continuously, one after another, independent of the annual pillar change. The yearly number in those tables is simply a computational key, not the energetic year pillar itself.
We have 60 possible stem and branch combinations, so the cycle repeats every 60 days. In the same way, the year cycle repeats every 60 years — for example, 1924 and 1984 are both Jia Zi years.
It is also worth mentioning that some calculators found online use the solar calendar as the beginning of the year. This may change not only the stem and branch of the year, but in some cases also the stem and branch of the month.
It may even alter the transition dates of the divisions / Heavenly and Earthly Guest Qi.
So it is always worth knowing which calculator or calendar system you are using.
However, this does not affect the stem and branch of the day.