National guard and military typically fall under temporary authority of FEMA, IIRC, and sometimes even the police will. Except in Colorado that is unconstitutional, and FEMA respects that, as technically while they are civilian government, they are military oriented, thus per state constitution all military falls under civilian authority, which then places the liability for inappropriate conduct by such forces on the shoulders of the civilian leaders, who do not have absolute authority.
This is a bit of a yes and a no, Military force must remain under military control, civilian authority may have no control over them, but that's the reason agencies and organizations have liaisons and we have an ICS.
Basically National Guard or Federal military personnel can't have a group leader that's a civilian, when the NG or Federal forces show up they bring their whole chain-of-command with them, and FEMA may not even be in-charge when the Guard arrives, a simple Fire Chief may be, but under ICS guidelines if he retains specialized training for the event then he is IC (Incident Commander), and there may be multiple IC's during an operation, due to multiple situations, one incharge of personnel preforming rescue operations, one in-charge of ensure security, one in-charge of ensuring gas, water, sewage, ect.. are off, one in-charge of triage, ect...
CAP/USAFAUX can not have any military personnel in control of our personnel or operations because we're civil personnel, but in return to this we can not have any non-CAP personnel in control because we're an auxiliary. The organization is in a unique placement to have access to DoD and DHS logistics and support but without going through FEMA, and we can operate independently of the Federal Government.
It all falls into the ICS (Incident Command System).
See CAP/USAFAUX can't move on a Federal/DOD mission unless directed by MCSS or AFRCC, but the organization can preform missions under the "Corporate Mission" label, but under this facet they lack support of DoD/DHS because it isn't a Federal mission, and lacks an actual AFRCC/MCSS mission number, but local units (i.e. a squadron or wing) may activate it's personnel within it's AO without either AFRCC/MCSS or SEMA/CEMA support or permission, because each unit is self sustainable and self contained in, but the operations, but the circumstances in which the unit is activated must be justifiable.
So in the long run CAP/USAFAUX's basic point of existence is to help augment and be a "force multiplier" to a state or communities assets and even usher in faster support of FEMA or the military.
The way ICS works is when a disaster strike whomever is on the scene first is the Incident Commander (so in a nut shell if the police show up at a fire first, the officer in-charge is IC until the Fire Department arrives, so the cops just secure a perimeter, setup an IC post and if any police are EMT trained preform basic triage and the officer relinquishes command the the Fire Chief but the officer may still remain an IC or a member of the ICT "Incident Command Team" as a IC or assistant IC whom is in-charge of perimeter security and investigation into the inccident) and until support arrives that person is the IC, unless he relinquishes command to another individual (for a reason such as sleep deprivation, to eat, or to assist in another operation), so as I said before a simple Fire Chief or Police Chief may be the Incident Commander for a while until someone on the SEMA/CEMA CoC calls up FEMA/DHS/AFRCC and requests support, takes a call from the Governor to get other states or Federal military support, has to do with states rights and ensuring Posse Comitatus is upheld.
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