OK, let's say your power goes out. You get it back with a generator, but even though your power is now running, your internet is still down, so you can't access Apex Fusion. But both your Apex and your home network/wifi are working because your house is on generator power. Or if for some reason your wifi is out but your router is working, you can run a cable between the router and the Apex.
In either case, you just need to then access Apex Local, and turn individual devices on and off from there. To do this, open a web browser and navigate to 'apex.local' if you haven't ever renamed your apex system, or to '[yourapexname].local' if you have renamed it. Or you can use '[yourapexlocalipaddress]/apex/dash.' If you've never used Apex Local, it's basically the built-in version of Apex Fusion. However the tiles won't automatically be arranged the same as with Apex Fusion; you'll have to rearrange them and probably pull some out of the hidden tiles area.