The constellation is looking at the solar calendar. The year you were born, September is the third day of the lunar calendar, and the corresponding solar calendar is your constellation.
Libra 1/2 1 ~ 2/ 18 Leo July 23rd to August 23rd.
Pisces 2/ 19 ~ 3/20 Virgo 8/24 ~ 9/22
Aries 3/2 1 ~ 4/20 Libra 9/23 ~ 10/23
Taurus 4/2 1 ~ 5/2 1 Scorpio10/24 ~1/22.
Gemini 5/22 ~ 6/2 1 Sagittarius11/23 ~121
Cancer 6/22 ~ 7/22 Capricorn 12/22 ~ 1/20