In the simulator I operate (B737-300 Category D Full Flight), a flame out initiated on the instructor panel gives instant loss of thrust and a yaw and roll in the direction of the "dead" engine. The N1 and N2 decay until eventually the N2 and N1 show low numbers but continue to rotate slowly under influence of forward speed. There is no vibration. The follow up checklists do not require the crew to pull the fire handles.
There is an item on the instructor panel annotated "Engine Seizure." When actuated, there is instant loud engine noise associated with the engine running down and seizing. At the same time there is the expected yaw and roll towards the seized engine. There is severe vibration which is absolutly unmistakeable physically as well showing up on the relevant vibration indicator. .
In this simulator the N1 will quickly fall to zero caused by the failure of the drive shaft from the accessories gear box, while the N2 will run down more slowly. It is the zero reading on the N1 that is a characteristic of a seized rotor. That, and the severe vibration on that engine that would trigger the Severe Damage checklist rather than a mere engine flameout checklist.
Be careful here if the vibration indicators are EFIS type and not analogue. The needle on the EFIS dial is very small. Beyond a certain vibration limit that needle vanishes off screen. I believe that was one of the problems associated with the Boeing 737-400 crash at East Midlands where mis-identification of the failed engine occurred. In this event the EFIS vibration indicator needle disappeared off screen because it had registered a high reading beyond the capability of the vibration system and thus showed no reading at all on the gauge. It is wise therefore to look for corroborative evidence of severe damage or otherwise rather than rely solely on one source of information
See:
https://en.wikipedia.org/wiki/Kegworth_air_disaster
One extract from that report stated:"The vibration indicators were smaller than on the previous versions of the 737 in which the pilots had the majority of their experience. The dials on the two vibration gauges (one for each engine) were small and the LED needle went around the outside of the dial as opposed to the inside of the dial as in the previous 737 series aircraft. The pilots had received no simulator training on the new model, as no simulator for the 737-400 existed in the UK at that time. At the time, vibration indicators were known for being unreliable[3]:69–70 (and normally ignored by pilots), but unknown to the pilots, this was one of the first aircraft to have a very accurate vibration readout."
Post No 2 says it all. If your simulator has the N1 and N2 gauges falling to zero readings simultaneously when on the instructor panel the instructor has selected a simple flameout engine failure, this would suggest the simulator fidelity fails to meet that of a Level D category full flight simulator. Your instructor should be aware of this. If your simulator is a no motion operation then there will be no vibration present. This should have been briefed by the instructor concerned.
Be aware that pedantic simulator instructors exist and you could court retribution if you attempt to argue with these type of characters. A fact of life in simulator training. The QRH/FCOM are your friends when it comes to differences of technical opinion.