When creating a new incident, the resolved time is set immeaditly and an update for the field shows in the activity stream.
The default value of the active field on the incident table is set to false. This is done through a dictionary override. When active is false, an out of box business rule sets the closed_at value an custom business rule is setting the resolved_at date from the closed_at date.
Navigate to the sys_dictionary record for the active field on the Task [task] table and search for a dictionary override for the Incident [incident] table. Ensure the default value is not set to false.