Splenium tumors

Crossman and Neary write that...
"Destruction of the splenium of the corpus callosum by stroke or tumour leads to the posterior disconnection syndrome of alexia without agraphia. Such individuals speak and write without difficulty but cannot understand written material (alexia). Disconnection of visual processing in the right hemisphere from the verbal processing of the dominant left hemisphere is thought to explain the syndrome"

I thought that visual processing was not dominant to one hemisphere and that if it was it was dominant to the left hemisphere anyway because more people have stronger left eyes. I am aware that language processing occurs mainly in the left hemisphere...but nonetheless I am confused.

Why then do people who suffer from splenium tumours find reading difficult? thanks