Was looking into some parts of this as even the authorities to respond an emergency vary by province.
BC - A person may be conscripted to fight a forest fire under the BC Wildfire Act
AB - used to be part of the Forest Prairie Protection Act. I see in the 1972 version (Section 23) but not the 2000 version.
Other jurisdictions have had/used similar powers in the past - YK, NWT, ON
So if the powers are not a municipal level, and varied by the provincial....what is required to activate the Federal powers? I've never delved into that side of things mostly because I'm closer to the shovel pusher than 4-star general in charge...but it appears this is the legislation:
Canada’s Emergencies Act
www.canada.ca
It's a heck of a challenge though to understand what local capacity might be available to support (local knowledge is priceless) while dealing with a populace that is most affected. So like the CAF you need distributed knowledge of the generic principals - ICS in the case of disaster response - while you try to mobilize additional support form unaffected areas. Unfortunately it's not even as simple as take Toronto Police force and send them to a Vancouver earthquake as you have to still address Toronto manpower needs and only a portion of Toronto can go....which means your roster numbers need to be much larger than your deployment force.
It's a heck of a legal, and jurisdictional mess. Thankfully it's not the job of the CAF to resolve all Canadian emergencies but to @Kirhill point above somehow it needs to get sorted out.