BUT he had other children after 1600 so didn't die in 1590
ALSO, he was the son of William Oliver of Tottington, not Ralph.
All this is proved by the William Smith of West Chiltington's Will, who names a lot of people in the area and states the connection of some of his relatives, including his own parents.
From William Smith's Will of 1635
He states this at the bottom of the Will
William Smith buried Saturday 5th of May 1571 was married to Joanne the eldest daughter of John Searle of Bockinge ? leaving issue
Thomas
William the testator
Johanne who married Thomas, son of William Oliver of Tottington in Lyminster
who had issue
Johane,
Alice,
William,
Richard,
Thomas
Edward
William stated in his Will that Alice was the wife of Hugh Penfold and named their children and also instructed Hug hto use the money to build a school in West Chiltington, which still exists.