Front trigger fires the center barrel. Then the rear trigger fires the left barrel and then fires the right barrel. One version is a true side plate single trigger for the outside barrels and a trigger plate action for the middle barrel. The box lock version looks to be a hideously complex. Single trigger version fires all three barrels in a set order. Non selective firing order.
I have seen the Italian tri barrel but not that interested in them. The one I held was as dynamic as a fence post. It was a 12 to be fair. So maybe the .410 would be better. The ones sold by Holts auctions have gone for about retail.