The procedure I was taught for an engine failiure after take off with a Handling Pilot and a Non-handling pilot.
NHP "Engine failure No1/2.
HP Confirms engine failiure No 1/2
HP "Retard No 1/2
NHP places his hand on the appropiate throttle. "No 1/2."
HP confirms that it is the correct throttle and the throttle is retarded.
This would take a lot longer than the five seconds shown on the FDA of this aircraft. That five seconds suggests that the NHP acted independently.
The sounds of silence at multi engine training schools where the wrong feathering button has been pressed are legend.
As a previous poster has mentioned it is easy to rush an incident into an emergency.