In Vedic astrology, the sidereal zodaic, the band of stars surrounding the Sun's apparent path in the sky, is divided into 12 equal Rashis or zodiac signs. A person's Janma Rashi is the zodiac sign that the Moon appears in at the time of their birth. And a person's Janma Lagna is the zodiac sign that appears at the Eastern horizon at the time of their birth. For example, my Janma Rashi is Rishabha or Taurus, and my Janma Lagna is Simha or Leo; see my birthchart here. (I actually have the same Nakshatra and Rashi as Krishna!)
Now in my case, my Janma Rashi is different from my Janma Lagna, but based on scriptural descriptions of their births, I found out that in the case of Rama and Krishna they're the same. Rama had Karkata Rashi and Karkata Lagna, and Krishna had Ribhasa Rashi and Rishabha Lagna; see this answer. And I just found out that Chaitanya Mahaprabhu, whom Gaudiya Vaishnavas consider to be an incarnation, had Simha Rashi and Simha Lagna. And Ramanujacharya, whom Sri Vaishnavas (like myself) consider to be an incarnation, had Karkata Rashi and Karkata Lagna, just like Rama!
So my question is, is there some kind of rule that all incarnations of Vishnu have their Janma Rashi and Janma Lagna as the same? Now if someone's Janma Rashi is the same as their Janma Lagna, that would mean that at time of their birth, the moon was aligned with a certain zodiac sign, and the Eastern horizon was aligned with the same zodiac sign, so the moon and the Eastern horizon were aligned with each other. That means that all the figures mentioned above were born at moonrise, i.e. the time when the moon first emerges in the sky (which is not necessarily at night).
So are there any scriptures which say that incarnations of Vishnu are always born at moonrise? By the way, if I'm not mistaken the orbit of the moon relative to the Earth and the rotation of the Earth relative to the fixed stars (in the sidereal zodiac) are completely uncorrelated, so the probability that Rama, Krishna, Chaitanya Mahaprabhu, and Ramanujacharya would all have this property by chance is less than 1 in 20,000. So clearly something is going on here. Do any works on Vedic astrology say that there's something special about people born at moonrise, and do all incarnations of Vishnu belong to this category? What about at least the Purna Avataras?