I will give another reason why the bottom barrel should be fired first.
Last week, I did a gun fitting with pattern testing for a young man who shoots trap in the High School Clay Target League.
This young man shoots left handed and is left eye dominant. He was shooting an SKB TT-15 Double Trap (over/under).
I noted that he initially canted the gun such that the lower barrel patterned several inches to the right of the point of aim at 16 yards.
Thinking about that, the upper barrel shows Point of Aim = Point of Impact, but the lower barrel does not at 16 yards.
An error such as this will be exacerbated as range increases.
Another reason to fire the lower barrel first is that any error in your gun mount or technique is more pronounced in the pattern of the lower barrel.
In other words, the upper barrel is more accurate and should be used on your longer shots.