Putin wishes to see NATO weakened so that he can assert more control over Eastern European countries. Since he has already influenced the 2016 elections, influencing cabinet member choices would be a logical next step in return for development opportunities and financing from Putin cronies. Putin already has a Mediterranean seaport in Eastern Syria, and Trump supported his incursion into the Ukraine, so he's well on his way. It would be foolish to believe that Putin doesn't have any influence on Trump. Not quite to the point of choosing our secretary of state, but definitely influence.
I differ on the point of choosing our Secretary of State. Just who would think of the head of Exxon as the nominee otherwise?
In all honesty, I believe that Rex Tillerson may not receive confirmation by a Republican controlled congress primarily because of his Russian ties. It was one thing to accept Russian assistance in gaining the presidency for their party, but quite another for Trump's cronyistic (Wiktionary) choice for Sec. of State to be confirmed. There are limits to even Putin's influence. Admittedly, I have been wrong before ... Trump as president ... I trusted the media a bit too much. Since a hundred million eligible voters chose not to do so, I'd say I had plenty of company even though I did vote.