"If a team has multiple reactions to the same trigger, only one is used at a time. Then the other team can use a reaction. A team with multiple reactions to the same trigger can use them in the order it chooses, as long as the other team has a chance to use a reaction in between."
This seems to imply that both teams can have reaction to the same trigger and that they should take turns activating triggers. But who gets to go first?
"If you do not use any of your reactions to a particular trigger, you can’t later react upon seeing further reactions to the same trigger."
I can't quite figure out how this plays. The way i read it is that once you have turned down chance to play a reaction to a trigger, i.e. before or between reactions from the opposing team, you cannot later choose to play a reaction to that trigger. I'll try to illustrate it with an example:
1. Trigger happens
2. Team 1 declines to play a reaction
3. Team 2 plays a reaction
4. Team 1 not allowed to play a reaction due to this rule
5. Team 2 plays another reaction
If this is the correct interpretation we return to the question of who has to react first. In the example above team 2 would know when playing their first reaction that they will be able to play the second reaction unobstructed.