Person buys a product, or downloads some software - that unknowing to them, was reaching out to a central server elsewhere to establish a network tunnel. And over that tunnel, the other server routes traffic onto that person's home network. Which can then of course go onto the internet, and it appears like the traffic originated from their home internet connection.
Other people rent access to this network. The goal being, you have surreptitious access to appear as any one of tens of thousands of home network IP addresses on the public internet. Bad guys can use this to rotate through many different IP addresses when their access gets blocked because of malicious (or benign but unwanted) behavior on the internet. Residential IP addresses are more 'valuable' because they don't have the negative connotation that datacentre and commercial IPs can have, and they can be spread geographically or across many ISPs.
A very common way for people being a part of these residential proxy networks is by buying dodgy streaming boxes, and also installing shady apps on TV app marketplaces.
Such as ignoring web scraping countermeasures, and DDoS.
* I initially thought this meant someone in the WH network was using commercial proxies to appear as if they were exiting from a different network (which would align with "some user is firing up a proxy on their phone to exit in a different location")
* But then the description of residential proxies seemed to align more with traffic hitting an endpoint in the White House, and _exiting_ from the network there. But this didn't explain the timing (why isn't it 24/7).
* Finally it sounds like some person, legitimately on the WH network, has a device (cell phone, TV, whatever) that, when activated, is proxying outside traffic into the WH network.
Many questionable TV streaming boxes pretend to deliver you video, but in reality they are also piggy backing on your personal ISP to power those companies.
+ Sketchy Apps
+ Malware
+ Weird Android Variants
> Residential proxy services sell access to everyday devices, letting customers send traffic through them so it appears to come from that device's network.