Apart from the pH and sugar your tomatoes bring (as mentioned in the comments), I think there's a third part to the explanation - you're likely adding more yeast!
In Wild Fermentation by Sandor Ellix Katz, there's a section on how to get a sourdough starter started. They suggest that if your starter never gets going, you put some pieces of fruit - like apples or grapes - in it, and the wild yeast which almost invariably inhabit the peel of the fruit will get the fermentation going. There's no reason why tomatoes wouldn't be likewise inhabited.
I suppose you test this hypothesis by making two doughs, one to which you add fresh tomatoes, and one where you add tomatoes from the same source which have been cooked.