evacuee
A person who has evacuated from a dangerous place, such as a disaster area or conflict zone.
After the earthquake, many evacuees gathered in the gymnasium.
The evacuees needed blankets and food.
避難者 specifically means someone who has evacuated to a shelter, whereas 被災者 refers more broadly to anyone harmed by the disaster, evacuated or not.
Compound of 避難 (ひなん, 'evacuation, taking refuge') + 者 (しゃ, 'person').