During the years -------,he worked as a doctor inthe hospita

During the years,he worked as a doctor in the hospital.“that followed”是一个定语从句,that 如果省略,就变成了非谓语动词范畴,强调“被动”的含义,但 句子主语he,follow 与 years之间不存在主、被动关系,所以这里的"that"不可以省略
With the situation changed,the young workers must study advanced technology.中的situation是“被改变”,非谓语动词中的“过去分词”强调“被动”的意味,与With构成伴随状语,所以这里不可以加“that”,楼主在此处对语法现象的判断发生了混淆.