I have been familiar with Tertullian.
He was both right, and wrong. Pompeii was a particularly affluent city, a retreat of the wealthy. Are you familiar with the Starz TV series “Spartacus?” It is full of violence and nudity and perversion…so was the Rome. Pompeii may have been particularly bad. Spartacus happened about 150 years earlier, on the North side of the volcano. Pompeii was to the south.
In Pompeii, there were Christians who saw Jesus. One instance of graffiti that was found around Pompeii was an Upside-down Pentagram with the Hebrew word for “When God totally destroys something.” Like Sodom.
Tertullian was both right and wrong. Given pagans were wicked, rejecting God, being obstinate, in the face of Christianity, that may have brought about God’s judgement.