The American Red Cross has a course in Psychological First Aid for its volunteers, focusing on serving clients undergoing stress in disasters. I found it to be a very worthwhile course, and the Red Cross recently made it a required / recommended course for higher level (supervisor) volunteers. Red Cross has a significant disaster health services commitment, and part of that is mental health services.
Folks will lose their homes and possessions, some may lose family and loved ones. There can be depression, sadness, tuning out, anger - you want watch for signs and deal with them as best you can. Any disaster causes disruption, we all deal with that kind of stress differently. And people bring their pre-existing physical and mental health issues to your shelter or service.