—When did your cousin begin to show his interest in medicine

这不是强调句!
如果用强调句,那么去掉it is..that...这个框架,结构是会依然完整的.比如：
It is apple that I like most.→I like apple most.
事实上,你的句子若用强调句型,应该是：
It was on Saturday that she noticed her uncle experimenting on a frog in his lab.
（去掉框架）She noticed her uncle experimenting on a frog in his lab on Saturday.
注意到没有?原句是没有介词on的,所以,所以它只是一个定语从句,先行词为时间Saturday,由关系副词when引导

What 是肯定不对，that 就只能回答时间｛因为那样的话定语从句去掉就只剩 It was a Saturday了｝所以选C。
这里when不是问的，而是类似 “是在…的时候” 的感觉。