Why do tomatoes react with sourdough starter? I sometimes make sourdough and have found by accident that by adding fresh tomatoes to the dough, it seems to swell substantially more during proving, or more quickly.

There must be some chemical reaction and I just wondered if anyone knows more about it?
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.