Great question! Both of these creatures had fire-related meanings in classical mythology. The phoenix never died, but instead, built a nest when it was old and burned itself up. When the fire was gone, a new/young phoenix rose from the ashes. This would symbolize both that the firemen wouldn't be hurt by the flames, and that their burning is intended as a kind of regeneration. A new society is being born by their efforts.
The word "salamander" comes from the Greek, and means "fire animal." Salamanders were thought to be born from fire. Therefore, both animals were associated with fire, and with new beginnings from the flames, which would be very appropriate for this sort of fireman.