Rex Tillerson most likely has a lot of lawyers that he consults to ensure that things that he does are legal, or at least that he won't face severe consequences if he is arrested. Most likely what he's doing is legal, but regardless, this is not the type of behavior that we should expect from our Secretary of State. The Secretary of State should care about the country enough to pay his or her fair share in taxes, and not hide his money offshore.
There is no question that Rex Tillerson has a lot of money. After all, he has been running a corporation with a net worth greater than many countries. That fact alone is not proof, but is a good indicator that he is not making efforts to illegally hide money in the Bahamas. He has enough money already. Why put it all at risk, just to hide a little more?
Rex Tillerson, the chief executive of Exxon Mobile, is an odd and controversial choice for secretary of state. There is some information that points to him being director of a Bahama-based US/Russian oil company. This certainly justifies a more intense look at his activity, but, as yet, there is not hard evidence he has done anything illegal.
The business world is complicated. There are rules about what people can do and about what is legal and what is not legal. Even if a person does everything right, there are always opponents that will make ridiculous assertions against them. People do this for political gain, even if it is not true, like in Tillerson's case.