Maybe I can clarify myself abit better.
Its the behavior regarding what was discussed in the apology.
If the apology was say about breaking a mug while drunk and they apologize saying they sorry won't do it again etc etc. If they keep breaking a mug while drunk then it is not sincere to me. Even if he is nice about everything else. He still was not sincere about his apology.
Genuinely sorry people tend to try and make it up so won't "forget" what they promised.
Silly example but I hope it makes my point.