Here are a few additional points to give more context how this volunteering is organized in Germany:

1. Employers have to allow their employees to participate in aid missions and also have to pay them for the time they spend volunteering in an emergency. Employers can get the paid wages back from the respective authority.

2. In my experience the mentioned organizations are often youth organizations similar to sports clubs and are doing a lot of social work apart from emergency, rescue and disaster missions.

3. Historically it wasn't completely voluntary. When I was young every male citizen had to pay a fee if they didn't participate. This was abolished eventually, because of gender equality. Also, compulsory military service (when we still had it) could be avoided by volunteering at least four years in disaster relief.