What is the psychological basis for people coming together during a disaster or major event?
This article might be helpful. In particular, humans need social connections (according to Maslow's hierarchy of needs). Stress initiates people to come together. It was thought that women would come together during disaster and men would fight (i.e. the fight and flight response). However men also come together during disaster.

A distinction must be made between acute and chronic stress. Acute stress (e.g. once in a life time natural disasters) promote social bonding and connection. Chronic stress (e.g. smoking, ruminating a lot, etc.), however, does not seem to produce the same effect. When the acute stress is removed, there is no imminent need for social bonding with strangers.

From a biological basis, it seems that oxytocin might play a key role. In particular, oxytocin is released as a reaction to a social experience. So if a people see others in distress they may release oxytocin which promotes prosocial behavior.