So I saw this and that last part I disagree with a little. Formal Apology says "after the next time this game your Honor is below its starting value, you have a tea ceremony; gain 5 Honor." (emphasis mine) So that leads me to believe that it doesn't matter if your honor is currently below your starting honor because that is the current time and not the next time. So you would not gain the honor immediately if your honor is below the your starting honor.
Formal Apology timing cont
A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
So I saw this and that last part I disagree with a little. Formal Apology says "after the next time this game your Honor is below its starting value, you have a tea ceremony; gain 5 Honor." (emphasis mine) So that leads me to believe that it doesn't matter if your honor is currently below your starting honor because that is the current time and not the next time. So you would not gain the honor immediately if your honor is below the your starting honor.
"Next" in this case is not an event caused by a change in honor totals, but instead a constant check referring to any point in the future. Therefore, if you're already below your starting honor, one second after Formal Apology is in play is the "next" time you're below your starting honor, and it will trigger.
On: Formal Apology