JESUS (Origins of His Name) https://youtu.be/cI4FfsL9urs
The mix up comes from us forgetting the sign Virgo and the position of the sun in that sign at the time. Under the tropical zodiac, the Sun transits this area on average between August 23 and September 22, and under the sidereal zodiac the sun transits the constellation of Virgo from September 17 to October 17. So you are right. This is why.