Whether using a company ops manual or not, standard rt is required from the rt manual and not operator specific. Otherwise that would confuse the heck out of everyone. Within the rt manual there is latitude to apply company policy though. Our company policy also allows an amount of discretion on the captains part.
I would not expect critisism for declaring a mayday for an engine failure (given that this is something we regularly do in the sim!). I would expect critisism for NOT declaring an emergency though.