Did he write about it later in his life, using other people's stories as a source, or did he write about it using his own knowledge? Or did he do something else? (I can't imagine him writing about it at the age of 9)
As far as I am aware, he only started his writing career in 98 AD.
Thanks!
Tacitus was a prominent member of the court of Hadrian, and was a member of the senatorial class. He would have had access to a variety of information, through records and letters, but most importantly through word of mouth.
This word of mouth was significant, as Nero, and then later Domition, did not get along with the senatorial class at all. Thus, Tacitus is gathering a whole much of his information from hostile sources. His writings on Seneca reflect the much larger theme of his annals, which serves 'To address the larger truths of tyranny and political freedom'.
He is harsh on Seneca because he believes that not only did he allow Nero to indulge in his distinctly unorthodox and non-traditional vices, but claims the elderly senator was immensily hypocritical. Seneca was a stoic, and Tacitus portrays him as having instilled none of his values onto the young emperor.
To summarise, Tacitus uses Seneca as a vehicle to get across some of his own moralistic points. He will have had an understanding of Seneca from word of mouth, viewing imperial letters and notes, and perhaps even the work of Seneca himself.