Let's consider an extreme case. This site reports that the ionic radius (of Na+) is 116×10−12⋅m; the atomic radius of sodium is 154×10−12⋅m. (I use these numbers, because as physical scientists we are OBLIGED to use numerical data!)
Now the atomic radius is by definition the distance from the nucleus to the radius described by its valence electron.....And of course for sodium, the valence electron is a 3s electron, (1s22s22p63s1). Now of course 3s electrons describe a greater radius than 2s or 2p, and thus the ionic radius necessarily reduces upon oxidation.
On the other hand, chlorine has an atomic radius of 99×10−12⋅m; but chloride anion has a radius of 167×10−12⋅m. Here, reduction, addition of an electron to the valence shell GREATLY expands the ionic radius of the ANION with respect to the radius of the atom.
