The day (on which) he was inducted, he was not feeling well. 

The day (when) he was inducted, he was not feeling well. 

The day (that) he was inducted, he was not feeling well. 

I recognized him the moment (at which) I saw him. 

I recognized him the moment (when) I saw him. 

I recognized him the moment (that) I saw him. 

时间名词用作连词，其实就是定语从句省略关系副词后变来的。省略的目的是为了简练。本来这类连词就已经“不简练”了，如果再添上关系副词，就违背了简练原则。

我认为，括号部分可能是老师讲解用的，其实是累赘。所以，括号内的部分一律省掉。