I think that we see here a problem of some inconsistencies that exist in the rulings, which make it hard to form a consistent mental model, which is a prerequiste for programming.
In this case, the Mandarin was gained when a Royal Seal was in play, so both Mandarin's ability and the Royal Seal's ability trigger. As SSLY has pointed out, it shouldn't matter what happens to either after the fact that they triggered. So in this case the ruling is that it only matters where a card was when the trigger condition happened.
Just yesterday I asked a similar question on f.ds Start of turn question
. Here the trigger condition was "Start of turn", and to my surprise the answer (from Donald) was that in this case a card can arrive with a "Start of turn" trigger effect during the handling of other "Start of turn" effects, and it is still considered to be handled this turn.
So it seems that the game for some triggers only considers the exact trigger time, while for others it considers the whole time when the triggers are handled. I have no idea which triggers actually fall into what category.
Clearly the game used a 'considers the whole time when the triggers are handled' approach for Royal Seal, which was incorrect in this case. As SSLY pointed out, the interaction of Estate-Mint with Hoard on turn 12 was based on the 'only considers the exact trigger time' model.
I don't see how a player can understand what effect uses what model.