You weren't actually wrong, there are different meanings of fall/autumn.
Here is Merriam-Webster's definition of autumn:
1 : the season between summer and winter comprising in the northern hemisphere usually the months of September, October, and November or as reckoned astronomically extending from the September equinox to the December solstice —called also fall
Dict.org definition of fall/autumn:
1. The third season of the year, or the season between summer
and winter, often called "the fall." Astronomically, it
begins in the northern temperate zone at the autumnal
equinox, about September 23, and ends at the winter
solstice, about December 23; but in popular language,
autumn, in America, comprises September, October, and
November.
[1913 Webster]
Erica