It isn't only the just man's words, but his whole life that says, "God will take care of me." "Because his life is not like other men's, and different are his ways" (v 15).
Figuring out how to live in the different way that says, "God will take care of me," can be tricky. To be a person of true hope -- full-bodied, theological virtue-type hope -- is hard, in part because hope is so easy to simulate.
It can be simulated by presumption, of course, if we conclude our salvation is certain by, so to speak, subtracting God out of the equation. You can't have faith in a deterministic process.
It can also be simulated by expectation. Unlike presumption, expectation isn't sinful per se, but it can confuse us into not growing in true hope.
Hope, properly speaking, is founded upon God and God alone; it is also a virtue that comes from God alone. The injunction, "Hope in God," is perhaps more true than we realize. What can properly be called "my hope" really is in God; His goodness and His power contain my hope, produce it, and provide it.
Expectation, though, is founded upon my judgment. Having considered all the information available to me, I determine the probabilities and effects of various outcomes, and so conclude what I can expect as a result. My expectation may depend on the action of another, even of God, but that dependence doesn't make it a hope. Hope is an absolute and complete dependence on another (the other must be God, or it's a foolish hope). My expectation of another depends on my evaluation of the person and the circumstances. As soon as I put something that is properly my own between me and the other, I am not talking in terms of hope.
Perhaps part of the reason most of us aren't likely to be put to a shameful death is that we don't much hope in God. We live, not in hope, but in expectation. We expect things of ourselves and of other humans, but we have learned not to expect things of God. That doesn't sound good, but I think it's the correct lesson; God has a way of doing the unexpected, and it's hard to construct expectations around that.
We're left busily expecting things today and tomorrow, and leaving all that hope in God stuff for after we're dead. A hope like that isn't likely to stir the wicked to revilement and torture.