Church leaders, as I have explained, are not historians or reliable sources of information period and can't be dated, I even mentioned this already, Ignatius, Polycarp, etc, are NOT historians.
The Nazarenes were not mentioned until the fifth century by a historian, as I said and remains true, as the Bible and its rejected Apocrypha are not historical, including the epistles mentionied.
I noticed you didn't mention a name, just assert that someone said that 10 historians of the first century mention Christianity. This is hardly true as not one did, in reality and I can only guess your author is being cute with facts to support preconceived notions of his, but he is wrong to claim that.
Chrestos was mentioned by, I believe Pliny, but that is disputed in academia as possibly interpolated and I don't think Pliny was first century but if I am mistaken it's irrelevant as he had no idea what a Christian was or who was Chrestos.
Philo of Alexandria, contemporary of Jesus PBUH from Egypt and a Jewish historian and philosopher also contemporary with Josephus never mentioned Christianity and he would have known as a nobleman in the Roman Empire and relative of the Biblical Berenice.
Josephus mentioned Philo, he was an Aristocrat of the Jewish Alexander family and his brother a Roman administrator of some sort, prefect I think.