No, from a game mechanics perspective, it is a semi-random event. You target the enemy by pressing a button (Caped Soul removes his mask) and using the left analog stick to "aim", lock on (Caped Soul locks gazes with the enemy), release the button (or lose lock), and one of three things happens:
1) Red Cape (Caped Soul jumps into enemy, and it is killed)
2) Blue Cape (Caped Soul jumps into enemy and possesses it)
3) Refusal (Enemy breaks contact, becomes angry or runs away)
I say semi-random, because the probability will be based on the enemy's "level" compared to the Caped Soul. Lower-level enemies are more likely to be Red Cape'd, and higher-level enemies are more likely to refuse. There isn't any exchange of a cape. The colors are merely a way to tie into the legend. Visually, the Caped Soul's cape will become red as he jumps into an enemy on Red Cape, or blue as he jumps into an enemy on Blue Cape.
So from a game mechanics perspective, it isn't complicated -- you are just pressing a button and aiming. The rest is handled by the engine.