I cannot realy subscribe to the right way wrong way thing when dealing with double trigger double gun. Especially shotguns.

There are many situations where one might have cause to fire the barrels in different orders as they are choked differently.

If shooting driven Partridge, then one might wish to fire the choke barrel first and then the cylinder/1/4 barrel as the birds get closer. Crossing Grouse may well be dealt with the opposite way around. Going away birds open first choke second, incomers the other way around. Crossers either way depending on where one wants to kill them.

So IMHO there is no point in training to fire a double only in one order. Better to be entirly familier with the gun and to use it the way that suits best.
Personaly for deliberate fire with a D rifle I prefer to use the rear trigger first as I prefer the trigger angle and find that I have more feel for the break than the straighter front trigger blade.

I think however that in the end it comes down to personal preference and familarity.

Regards