Apologizing only when you get caught isn’t sorry. It’s damage control.

Timing is what tells people which one they are getting. An apology that arrives the moment somebody finds out is about your position rather than about them, and everybody can feel the difference even when nobody says so. Being sorry is what you felt before the discovery, and what you would have done about it if nobody had ever noticed.

If something you did is still unknown, say it before it surfaces, because that is the only version that carries weight. Lead with what you did and what you will do, not with how bad you feel. The early version costs less and buys more.