Of course they don't happen at the same time; the game ends the moment the bishop is captured. A pawn doesn't promote until its owner says what it promotes to.
The rules in the article already resolve the dilemma according to that interpretation; the Rules section says:
If a player promotes his last Pawn, he loses (as his Pawns are now extinct), unless he wins by extinction on that very move.
I don't know if that is something that was added later. It is the opposit from what we have in Atomic Chess, where it is forbidden to blow up your own royal, even if that takes out the opponent's one. In Tenjiku Shogi it is also possible to destroy both royals in the same move, by capturing a King that stands next to a Fire Demon with your own King. The historic rules don't mention what would happen in that case (as it of course never happens in practice).
The rules in the article already resolve the dilemma according to that interpretation; the Rules section says:
I don't know if that is something that was added later. It is the opposit from what we have in Atomic Chess, where it is forbidden to blow up your own royal, even if that takes out the opponent's one. In Tenjiku Shogi it is also possible to destroy both royals in the same move, by capturing a King that stands next to a Fire Demon with your own King. The historic rules don't mention what would happen in that case (as it of course never happens in practice).