that maybe what they are for but some double triggers will only fire in 1 order!
That is news to me, is it possible that you have confused single non-slective triggers with double? I have an AYA with a single non-slective trigger, fires right barrel first, then the left barrel on the second pull, no choice. But any two-trigger gun I have ever handled can fire the barrel that it is connected to independently of the other.
I am aware of one exception, a Czech made Brno O/U that had a complicated "hybrid" trigger mechanism, it could fire the bottom then the top barrel with two pulls of the front trigger or the top barrel only with a pull of the back trigger.