The idea of Vesuvius as a moral punishment is mainly an invention of 20th century cinema. There are two ancient reports that come within earshot of the same idea, but only within earshot. First is the extremely unreliable 3rd century report in Dion Cassius, 66.23.1 (tr. Cary):

Thus day was turned into night and light into darkness. Some thought that the Giants were rising again in revolt (for at this time many of their forms could be discerned in the smoke and, moreover, a sound as of trumpets was heard), while others believed that the whole universe was being resolved into chaos or fire. Therefore they fled ...

(The bit about Giants relates to the idea that the Giants were the children of Earth.)

Second is a 1st (or possibly early 2nd) century Jewish apocalyptic poem which sees earthquakes in Salamis and Paphos, and the eruption of Vesuvius, as Yahweh's vengeance for the crimes committed by the Romans in the Jewish War: Sibylline oracles 4.125-136:

And to Syria [the province, i.e. including Judaea] will come Rome's frontline fighter [i.e. Titus],
who with fire will burn Jerusalem's temple to the ground, and slaughter many
of the Jews, and will destroy the great broad land.
And then earthquakes will destroy Salamis [on Cyprus] and Paphos,
when the loud-roaring dark water will overwhelm Cyprus.
But when from Italy's cleft earth
fire shall be tumultuously cast into the broad sky,
and destroys many cities and men in flame,
and glowing ash fills the great aether,
and drops like red clay fall from the sky,
then [they will] recognise the wrath of the heavenly God,
because they wiped out the blameless tribe of the blessed.

The idea of linking the eruption to Roman moral vices is an invention of 20th century cinema. Here's one instance from Joan Collins, interviewed in Playboy in 1981 and quoted by Arthur Pomeroy in his book Then it was destroyed by the volcano (2008):

It's like the Roman Empire. Wasn't everyone running around just covered in syphilis? And then it was destroyed by the volcano.

Now, that's untrue on multiple counts, of course. But it's a picture based on novels and films about both Rome and Pompeii. Sienkiewicz's Quo vadis (1895) and the older film adaptations of it (1914, 1932, 1952) depicted a Rome full of debauchery, cruelty, and persecution of Christians, which was punished by the great fire of Rome in 64 CE. At the same time, Pompeii was also a popular theme thanks to Bulwer Lytton's 1832 novel The last days of Pompeii, which also had cinematic adaptations in 1913, 1935, and 1959. It featured evil Egyptian priests who get their comeuppance in the volcano eruption.

One poster for the 1959 blockbuster starring Steve Reeves reads

SEE! The Shameless Orgy As Drunken Pompeii Abandons Itself To The Goddess Isis

Another is headed

THE MIGHTY SPECTACLE OF A CITY THAT LIVED IN SIN AND DIED IN FLAME!

And another,

Pompeii! City Of The Pagan Hordes City Of Beast And Battles ... Of Revels And Orgies ... Of Spectacle And Splendor! The City That Lived In Sin ... And Died In Flame!

Chapter 1 of Pomeroy's book is a good overview of how this interpretation of Vesuvius developed over the last hundred-odd years.

Edit: corrected a disruptive typo.