I made a small explanation on Deepling bosses in this thread:
https://www.tibiaqa.com/12068/how-many-deepling-bosses-can-i-kill-per-one-week-in-liquid-black-quest
If you check it, you will see that when to open a chest is a matter of strategy.
You can open a chest right after killing a boss, but then you will be giving up the possibility of killing the other bosses.
But, at the same time, if you kill more than 1 boss, and wait to open a chest after, you will be "owing" chests. Meaning that in future weeks, you will have to do Stage 2, just to be able to open chests in stage 3, from bosses you killed days before.
That happens because you can only open 1 chest per Stage 3, despite the amount of bosses you killed. So, if you kill all 3 bosses in a single stage 3, in the next one your options will be limited, because you will only be able to kill the one that you opened the chest of. The other 2 will be blocked, until you open their chests.