(I will preface this with "I do not believe in evolution in the modern political/scientific sense" but instead infer you to mean just the 'fantasy evolving' concept from so many stories. Assuming an evolution is based upon biological, chemical, and energetic interactions, at the least.)
Consider at the cellular level, if you will. A single cell is the equivalent of an industrial factory ― buying and selling. Taking in raw resources, processing, consuming, and shipping out the excess or waste products. A cell is almost all a warehouse, but also has its control towers and factory workers, things going on down at the atomic or subatomic level.
If evolution of a living creature is the intent, first look at the intricate nature of the cellular structure and function. It has already been suggested having a creature consume the energy/existence of another. Perhaps this is from one creature physically consuming the flesh (or maybe 'core') of a defeated enemy; or perhaps it is from some 'soul sucking' ability. But no matter what, I would again point to the previous paragraph ― how. How is this energy or essence or existence drawn in, consumed, processed, and utilized for the evolution?
I will for the sake of this premise, tactfully submit a fantasy evolve process would assuredly not take less than several hours. In human bodies alone, it takes the blood/circulatory system how long for a complete traversal? And this is not to say that if the energy sufficient for an evolution were passed into the bloodstream and dispersed that an evolve would occur right away. Consumption and digestion of the flesh/meat from a slain opponent is one thing; utility of this same energy or essence is another, at each cellular site.
Does an evolution only finish as 'complete' once each and every cell in the body has attained this same result? Or is the evolution something which it can consider nearly so, by a certain percentage of all cellular consumption of the same?
... in other words. I think maybe your hangups about a "System" assisting or forcing evolution is, maybe, because it "brute-force" changes a being. It's bypassing a normal consumptive/digestive/circulative/eliminative procedure, in favor of the surety of the change.