Here's how it works, for each phase:
1. Consider all players with unprocessed orders. Is the top order for everyone an Order Delay card? If so, process one OD card from everyone.
2. Process the top order from each player whose top order is not an order delay card.
3. Reverse the move order.
4. If there are still unprocessed orders, go to 1.
https://www.warlight.net/MultiPlayer?GameID=11157247 Turn 7.
The attack phase begins to process. Sultan has first move, Njord has second. First, we check if all player's first order is an Order Delay card. They aren't.
Now we process one order for each player. Sultan's first order is an Order Delay card, so he's skipped. Njord's first order is the attack from Kenya's so it's processed and removed from his pending orders list.
Move order reverses. Now Njord is first, Sultan second.
Both players top order is an OD card, so we process both of them.
Now we process one attack from everyone. Njord is first in the move order, so his transfer to Hong Kong goes first.
Seems to be the important part on how it works.