First of all, the requirement is being imposed on life origin theory, not the theory of Evolution. Secondly, all it really means is the theory of life origins has to be compatible with the way subsequent life works (i.e., the theory of Evolution.) What they mean by this is that a theory of life origins that explains a form of life NOT compatible with the subsequent evolution of that life form is not acceptable to the people offering the prize. An example of a life origin theory that was discontinuous with the theory of evolution might be one that posits some sort of silicon-based chemistry for the first life form. Obviously, this doesn't fit with the carbon-based chemistry of subsequent life forms that have existed.
So, back to my point, so long as one has a theory of origins of life that gives rise to life with the kind of biochemistry that the Theory of Evolution is compatible with, there is "continuity" between the two theories. It makes no difference what the explanatory model is for the origin of life, as long as it gives rise to something Evolution can subsequently work on.
So again, in that sense, Evolution is no more contingent upon how the first life form originated than Hydrology is contingent upon how water came into existence. Both are compatible with ALL explanations which result in the respectively required raw materials.