严重同意楼主的观点,此处应为that
It +be +强调部分 + that (who) + 主谓句.当强调的部分是人,且为句子的主语时,才用 "who",其余用that.
原句：My father did the experiment in the lab yesterday evening.
强调主语：It was my father who did the experiment in the lab yesterday evening.
强调宾语：It was the experiment that my father did in the lab yesterday evening.
强调时间：It was yesterday evening that my father did the experiment in the lab.(注意不用when)
强调地点：It was in the lab that my father did the experiment yesterday evening.
若是强调句,去掉It be… that之后,还应是一个完整的句子,而此处去掉强调句结构之后,此句依然是语法和逻辑都正确的句子,即In the library we read some books the day before yesterday.应该用that.
补充问题的回答：
这道题本身就有问题,如果用where：
Where did you come across Tom?
回答：In the library where we read some books the day before yesterday.
或者：We came across Tom in the library where we read some books the day before yesterday.
其实,我个人感觉用when更好：
Where did you come across Tom?
回答：In the library when we were reading some books the day before yesterday.
或者：We came across Tom in the library when we were reading some books the day before yesterday.
根本不可能用It was 句型.
如果出现It was 句型,个人意见还是用 that.
出这道题的人太变态,纯粹是为了考试而考试,不适用,逻辑上也讲不通.中国人出的英语题大多如此,害人,害人啊.