Global Rescue centres will be mini cities, 1000 to 2000 people all trained and willing to assist others. These mini cities will have full fledged infrastructures. This provides an additional benefit. People from poor regions can come to Global Rescue and learn to build and maintain water systems, sewer systems, power generation etc. Take this knowledge back with them to their home town or city and apply what they have learned there.
The Global Rescue centres will contain one or more of the following; hospitals, housing for the rescued, and workers. A sea port and a small airport. In later stages ships, aircraft, helicopters, religious centres (for all religions), and even cultural centres.
The rescued will first be received in the hospital, and remain under the care of the medical staff until released. Meanwhile the governments of their home countries will be notified, and arrange for transport home. After release from the hospital, people will be moved to their temporary homes. They will remain their until their respective governments can get their cities, and villages back to livable standards again, then they will be transported home.
During the times between disasters, Global Rescue's resources will be used to provide medical assistance to those in poorer areas, provide relief for famines (they are actually considered disasters). The centres can used as a staging or coordination centre for multiple relief agencies to coordinate their efforts.