Dielectric materials have electrons that can move. They do not get ripped out of their orbits which keep the material together (as long as no flames nor smoke occurs) but the orbits get stretched and the amount of stretching changes along the electric field. That makes the permittivity higher than vacuum permittivity. The phenomenon is called "dielectric polarization"

Changing field causes AC current to exist in the dielectric material.The reflected wave can be considered starting from that current.