I understand it was supposed to facilitate multiplayer
Actually, the original concept for the game was two different characters with different backstories, interpreting the events of the game from very different perspectives. Eventually the game grew enough the original story idea wouldn't work, but the characters remained (and character customisation was added).
How do I use this mechanic properly?
Answer for both characters, set an AI personality for the characters (if not done during character creation, it can be set after you open the Inner Chamber in the homestead, with the third star stone found or blood stone used), disable dual dialogues between the main characters in the options, or if you know a dual dialogue is coming up, separate the characters so the one not involved in the dialogue is too far away to be included (mostly useful if you set a random or contrary AI, and they keep blocking you from recruiting a companion, etc).
The Loyal AI will have the non-lead character always agree with the lead. You will make choices for the lead character, regardless of whether they have an AI personality set, or not.