Well, yes, of a necessity any extra-biblical account of Jesus would have to be after His death. That is unless you expect some other religious text to have prophesied His appearance ... and not all such references to Him are as recent as you suggest. Josephus being a case in point.
And given your chosen faith and field of study you should be well aware most mentions of Jesus in the Babylonian Talmud were redacted after prosecution of the Jews at the hand of the Roman Catholic church for being what they thought less than respectful of the individual in question in said tome.
The Koran and Talmud were written hundreds of years after the events. Not just "after his death". The source in Josephus (even if it wasn't a later insertion, which seems to be the case) is from 40 years later. And why is this statement true?
"of a necessity any extra-biblical account of Jesus would have to be after His death"
My faith isn't exactly "chosen". And being Jewish isn't a "faith"
And what do you think my field of study is?