Question:How does the ionosphere actually reflect radio waves?
It is basically the same as Total Internal Reflection for light in a glass block.
The Earth’s atmosphere is composed of different layers.
Although you cannot see any differences in the layers of the atmosphere, the different have different compositions of gas particles and are therefore different materials.
When radiowaves pass from one layer to another they are refracted.
If the angles are right then the radiowaves are completely reflected.
Refraction helps in this process because the radio waves are bent to shallower angle by each successive transition through the different layers making it more likely to hit a higher up layer above the critical angle.