"Shut down engine as soon as practical"
What does as soon as practical means ?
The Pilot action when given that instruction depends purely upon the situation the Pilot finds himself confronting.
The more you need that engine's power to safely fly the aircraft....the longer you take to comply if at all until safely on the ground.
The Caution Light color is "Amber" or "Yellow".....not RED. That alone should suggest the urgency that should be given to the problem.
That supposes there are no secondary indications of a problem....oil pressure, oil temperature, Ng Nf (N1, n2), exhaust temp, noises, vibrations, etc.
In my mind....engines are to be used as needed to allow as safe a landing of the aircraft as possible.
Memory serves me the such Emergency Drills are for shutting down one of two operating engines.....thus if already OEI....I am not going to shutdown that last engine until I am safely on the ground at the first suitable landing area.