I want to address the opening post and point out that it actually had two topics, only one of which has been addressed. It talked about reacting to an incident in general, and dealing with tank valve openings in particular. I would like to talk about incidents in general.
I attended a workshop for instructors at our dive shop a few years ago. It was conducted by a representative from the insurance agency, and it talked about the difference between an incident and an emergency. In our general scuba language, we tend to use the word "emergency" in discussing what they would not consider to be an emergency, and the point of the workshop was to suggest we both think about and teach a difference.
- An "event" or an "incident" during a scuba dive is something that is unanticipated and is usually not what is supposed to happen.
- An "emergency" occurs when we respond inappropriately to an event or incident.
The OP described a situation in which the diver responded appropriately to an incident. As a consequence, there was no emergency.
The workshop dwelt heavily on a similar situation, when a diver goes out of air. They consider that to be an incident, but we usually think of it as an emergency and treat it as such in our discussions. A diver's OW training spends a lot of time dealing with the appropriate choices a diver can make in a low on air or out of air situation. If merely low on air, the diver can usually make a controlled ascent to the surface. This can be done with very little air in the tank--close to none. The diver should be near a buddy and can do an air share as trained. The diver can do a CESA. The diver can do a controlled emergency ascent. All would be appropriate responses.
What happens too often, though, is the diver responds inappropriately by bolting to the surface, often holding the breath. That creates an emergency. The diver is all too likely to have an embolism, which can lead to death directly or to unconscious, which will result in death. In fact, a joint PADI/DAN study found that to be the number one preventable cause of scuba fatalities. ("Preventable" in this case means it can be prevented through proper training for an appropriate response to the incident.)
So is this just wordplay? The point is that teaching that kind of thinking will help make divers less prone to make a panicked and inappropriate choice that turns what they should be thinking of as in incident into an emergency.