^ Seconded
2.5 End-of-Match Procedure
If the match time limit is reached before a winner is determined, the player whose turn it is finishes his or her turn and five additional turns are played in total. This usually means that one player takes three turns and the other two, but a player taking extra turns may affect this. Team tournaments featuring multiple players playing together (such as Two-Headed Giant) use three turns instead of five.
So you get your current turn, plus five additional, regardless of whose turn it is or how those turns are generated. In this case, I'd argue that the turn in a sub-game is still a turn. Therefore, you get five total turns, regardless of how far down the rabbit hole you've gone.
This does introduce a problem with the possibility of playing Shahrazad on turn one of each subgame thus never actually hitting the end of any turns. However, this is addressed by the next clause:
Once time is called, no new games should begin.
Is a subgame considered a game? If so, then you can't start a new sub-game once time has been called so you will eventually win, lose, naturally draw, or run out of turns.
If a subgame is not considered a game... well, I can't imagine not considering it a game, so I won't go into it.
edit:
To actually answer your question, not just talk about Shahrazad and extra turns...
If players are in extra turns, what happens when you cast Shahrazad? How do you resolve it?
Given my second above point and the fact that the rules of the tournament are above the rules of the game, resolving Shahrazad would force you to do something that is against the rules of the tournament and should be punished in the same way as taking too many extra turns.
