As per NVMe Spec 1.3 below is the Async command desription:
Asynchronous events are used to notify host software of status, error, and health information as these events occur. To enable asynchronous events to be reported by the controller, host software needs to submit one or more Asynchronous Event Request commands to the controller. The controller specifies an event to the host by completing an Asynchronous Event Request command. Host software should expect that the controller may not execute the command immediately; the command should be completed when there is an event to be reported.
The Asynchronous Event Request command is submitted by host software to enable the reporting of asynchronous events from the controller. This command has no timeout. The controller posts a completion queue entry for this command when there is an asynchronous event to report to the host. If Asynchronous Event Request commands are outstanding when the controller is reset, the commands are aborted.
So I think you need to open simultaneously more than one command line and give more than maximum permitted async commands to verify the response.