Some people have Guillaume b. 1084, but not if the son Vulgrin was born in 1089!
Part of the reason for the later dates may also have been Guillaume III's gg-granddaughter, Matilda, b. around 1165, who m. Hugh IX de Lusignan. Most people have her as a daughter of Guillaume IV, but she is one generation further, being daughter of Vulgrin III, Guillaume IV's son.