Long story short, your birth time determines your rising sign (aka ascendant), as well as the rest of the planets in your chart.
Your ascendant is the sign that was rising over the eastern horizon when you were born, and while it changes signs every two hours, it takes only a minute for the sun to move from one sign to the next.
So, yes, “To get an accurate birth chart, you really need your birth time down to the minute,” the twins tell mbg.
Just a few minutes difference can change a lot, they add, noting that they themselves were actually born four minutes apart and have one slight variation in their charts. They add they have other friends who are also twins, born 10 minutes apart, who have different rising signs—which will result in a completely different outward personality and appearance, according to astrology.