Front trigger is usually set up with a lighter engagement, for the first shot.
Rear trigger is built with slightly greater engagement on the sear to withstand the recoil of the front trigger's barrel.
In shooting the rear (upper) barrel first, you are reversing the 'normal' routine of firing.

I know, Elmer used to say to fire the rear trigger first. Most double guns are not set up for that, though.

I am only repeating what I have read.
I've owned only double shotguns, never a CF DR. With the shotguns, it did not matter which bl. was fired first - no doubling unless 2 fingers were inside the TG.
This usually resulted in the need for a bandage to assist in stopping the bleeding.