Does the temperature of liquid ammonia stored at high pressure, room temperature suddenly drop to −33.35 °C when poured into a bowl?
The key to understanding what happens is that evaporation costs energy.

Changing the state of a liquid to a gas requires the input of energy: this is basic thermodynamics. This is in addition to any effects related to a change in temperature which also costs energy or releases energy.

When liquid ammonia evaporates to gaseous ammonia, energy is required from somewhere. If liquid ammonia at room temperature is poured into a bowl at room temperature it will want to evaporate as it is above its boiling point. But that evaporation requires an input of energy. That energy will come from the environment which consists of the bowl and the rest of the liquid. The only way to provide that energy is to cool the rest of the liquid and the bowl. This happens quickly and the temperature will often fall locally to below the boiling point of ammonia as there isn't enough time to equilibrate the temperature of the liquid with the temperature of the environment surrounding the bowl.

The net effect is that you will end up with some liquid ammonia at some temperature below its boiling point and a lot of gaseous ammonia (don't do this outside a good fume hood).

Forced evaporation of volatile liquids used to be used to freeze water via a similar process. For example, place a small bowl of water in a larger bowl of ether. Blow air onto the ether, which will evaporate, drawing energy from its environment (including the remaining ether and the bowl of water). The water will freeze if you used enough ether. I don't recommend doing this as ether is very flammable, but it was once a common demonstration of this process in chemistry classes.