In a word: Absolutely, positively, indubitably, yes. Now, having said that, you cannot "make sure the woman orgasms before he does", because if you have been reading you know that we tell people that each of us is responsible for our own orgasms. All any of us can do is to help our partner achieve them. Call it common courtesy or etiquette, it is a nice thing to help her enjoy the first, and last, if it is her desire, and then you and she together in between.

Is it mandatory that a man do this? No.

From the woman's side: YES! Many of us are most "receptive" immediately following orgasm. But, if the woman has taken control, let her go with it. She has something in mind.