SOP on all the fleets I have flown was to ALWAYS cross confirm with PF any thrust lever, engine master switch and fire push button BEFORE moving them. That surely is day-one of multi-engine flying training ??
That helicopter fire warning panel is awful design - just asking for problems. Like the engine instrument display panels in the B737 at Kegworth.
If ENG1 is failed and ENG2 is on fire, the ECAM will ask you to shut ENG2 down! - not something you want to do really.
....Unless Eng 2 is about to take out hydraulics, or fuel tank, or wing?. Depends on the situation - at least you can fly a FBW Airbus with no engines, and you might be able to restart Eng 1.
People much cleverer than I, have determined the ECAM priorities. They are probably right.