Question about opening chest after a summon fight ?

The party I was with in moogle all left without opening the chest, why is that exactly ?
I opened it since I was the last onein there but lost my key doing so, what does this mean exactly? That they're just entering without keys and hoping for a drop?

is a nutcharm an oblation ?
If so arent you supposed to get one if you have the key on you when you win? I didn't get one? I'm so confused how the rewards work in the summon battles
they got a nutcharm and gave it to an ls member and i lost my key and have to get it again now right? so so so confused

I think it only looks opened when you do it yourself, they all opened it but it doesn't look opened until you click it. Everyone has to open it separately.

ah ok, so i still have to get another key and open the chest etc? 10 oblations is a lot of wins, new to the summon fights lol

Every time you have a win you have to get the keystones again for Moogle fight. You are not assured a kupo nut if you win. I have several wins and only 1 nut and the CNJ wand.

The Ifrit fight is slightly different, you can do the fight without an inferno lamp but I don't think you get a chance at the good loot without it.

You don't always get a nut/totem when you win for some stupid reason