Not to drop a rain cloud over the parade, but that explanation describes why atoms get smaller as you move left-to-right across the periodic table. As Chemnerd explained, the nuclear pull increases and causes the electron cloud to contract, reducing the size of the cloud.
But, to answer your question about ion size, you need to first consider whether it is an anion or a cation. In a simplistic model, consider the impact of adding an extra electron to an atom to form an anion. The extra electron would repel the other electrons in the cloud, and it would expand. This explains why anions are bigger than the neutral atom. On the other hand, removal of an electron to form a cation results in a decrease in electron repulsion. This allows the electron cloud to contract, resulting in a smaller species. This means that cations are smaller than the nuetral element. Another factor that comes into play is the shell. If the electron being removed happens to be the last one in the shell, then the impact of size reduction is event greater, because a shell has been lost. This explains why alkali metal cations are so much smaller than their neutral element counterparts.
Hopefully this answers your question, assuming you meant ions when you typed it.