You can create a generic user custom field to hold the owner of the transition which changes issue's status to the specified status. This field is calculated (read-only) custom field.
To create a custom user field
- Navigate to JIRA Admin > Add-ons > Enhancer Plugin Menu > Custom Field Configuration and switch to User tab.
- Click on
button. - Fill the dialog
- Give a name to the custom field
- Select Status to hold date when the issue's status changed to this status.
- Specify First of Last whether the issue can re-visit this status (e.g. issue can be reopened and then changed to Critical Zone status again)
- And click Add Custom Field button. That's it.
This custom field can be used to sort or search in issue navigator.