Tillerson recently retired with all the accomplishments, respect, honours and money he would ever need. So to answer your question, he is the sort of good person who is a patriot willing to serve his country at the call and the urging of his new president instead of enjoying a leisurely retirement.

Should nobody of character or competence be willing to serve and to give back to the country so long as Trump is president?

This would condemn the US and its people to four or even eight years of gridlock, drift and decline and would not only harm America but also the western liberal democractic system because the US remains the leader and the chief financier of that system.

Cabinets and countries benefit when patriots with exceptional experience and accomplishments who don't need the gig and genuinely want to give back by serving their country before themselves answer the call of the president no matter who the president may be.