I don't recall there being a Buddhist teaching on an "ever-evolving consciousness". The consciousness changes, yes, but it doesn't "evolve". When some think of evolution, they think of a constant entity which is morphing over and over again into different shapes. The consciousness isn't something like that, and neither is the body or an animal. "Inconstancy" or "change" refers to things coming and going. The being that existed a second ago is not at all the same being that exists here and now. This "coming and going" occurs on various levels, and that's what really causes so-called evolution. When we look from a far-away distance, we fail to see each individual thing coming and going, instead we see one thing simply transforming, thus we create this idea of a being which is transforming.
This "evolution" of consciousness simply refers to different cittas (consciousnesses) coming and going in a process. The cittas that experience the jhanas are different than the ones which experience the immaterial states. When the fine-material-cittas cease and the proper conditions are present, the immaterial-cittas arise. I'm not very schooled in Abhidhamma, so I can't explain it very well. If you want to learn how consciousness works, read that. I recommend Bhikkhu Bodhi's "Abhidhamma Retreat" videos on youtube. Take notes and prepare for a headache, it's very difficult stuff to understand.
The realization that all things occur in a process, that all things come and go, is the realization of anicca. From that comes the realization of dukkha, and from that comes the realization of anatta.
"Eat little! Sleep little! Speak little! Whatever it may be of worldly habit, lessen them, go against their power. Don't just do as you like, don't indulge in your thought. Stop this slavish following. You must constantly go against the stream of ignorance. This is called "Discipline." When you discipline your heart, it becomes very dissatisfied and begins to struggle. It becomes restricted and oppressed. When the heart is prevented from doing what it wants to do, it starts wandering and struggling. Suffering becomes apparent to us."
— Ajahn Chah