That's thermite, not willie pete. Thermite is a point use incendiary made with aluminum, iron oxide, an ignition source, and binders. Willie pete is an area incendiary consisting of elemental phosphorous, which ignites on contact with air. As the demonstration in basic (mine was on the engine compartment of an old tank, burning through the armor covering the engine, the engine block, and the bottom armor, then several inches into the ground) illustrates, thermite is used to destroy vehicles, artillery, and equipment to which one has close access. White phosphorus is packed into mortar and artillery rounds to be scattered over a target area to ignite canvas, wood, and other flammable materials used by the enemy. This definition includes uniforms.
As has been mentioned, white phosphorus is very difficult to extinguish until it burns itself out. It will burn deep into flesh, drawing oxygen from the organic material around it. It is not supposed to be used against personnel, but if they are too close to the targeted materials (in their uniforms, which are the real target), tough luck.
We were trained to use it against forward arming points, motor pools, and supply dumps. It is against the rules to use it indiscriminately to just blanket an area, but Russia doesn't give a shit about rules.