Their baby Olivia arrived on the date she was expected. 依句點解

意思是指

他們的bb olivia 如期出生.

句中的she 是指 bb olivia, 不是母親
the date she was expected, 是指 她的 預期 出生日 (passive voice)

用過去式, 因為bb 已出生.

他們的bb olivia 如期出生.
The sentence must be:
Their baby Olivia arrived on the date she expected.
It means the event was already happened.

即係話母親如期望的日期產下女兒Olivia, 用past tense 即為第三者覆述或reported speech