When this happened is doubtful.

Foreign scholars often ascribe it to Augustus and find a special connexion between the first emperor and the chess-board town-plan.

But the architect Vitruvius, who dedicated his book to Augustus and who gives some brief notice to town-planning, urges strongly that towns should not be laid out on the chess-board pattern, but rather on an eight-sided or (as we might call it) star-shaped plan.[64] He would hardly have denounced a scheme which had been specially taken up by his patron, nor indeed does his criticism of the chess-board system sound as if he were denouncing a novelty in Italian building.
[64] i.

5 (21), 6 (28, 29).
On the other hand there seems no great difficulty in the idea that the regularization of the old Italian town-plan by Greek influence took place spontaneously in the late Republic.

We cannot, indeed, date the change.