Area Classification documentation is considered "PSM" documentation (Process Safety Management) and per government regulations need to be kept updated to actual plant configurations and conditions.
Typically in refineries there are studies that were done outlining the hazardous materials in the different areas, that is either done in house or by outside Engineering Companies. Then the Electrical Engineers (Either in house or outside Engineering Companies) in consultation with Process Engineers develope the Area Classification drawings in compliance with API 500 and NEC.
Someone from the Plant needs to have ownership of the documents for purposes of OSHA and PSM audits.
At our facility this rests with the Electrical Engineering Group, Other sites may have a central engineering group, or an E/I Maintenance group that does this function.