When evolving during gameplay, your offspring will change, but not your current animal.
Also, in the Demo you can't play as your offspring. The inheritance feature is disabled for the Prologue Demo.
I meant the editor was bugged for me. When I opened the editor after making an offspring, it would display the points I have ammassed during gameplay but after purchasing a part, it would reset to the value you get at the beginning of the game, so improving your creature was impossible. I think this was a bug and not intended.
But maybe it as already been fixed because I haven't played since 50 days. Still, please playtest again, gain some DNA points, try to customize an offspring with those newly gained points and see if it works.