I'm going to offer a big, fat "i Don't Know", because I truly do not know, and RW has never publicly said anything about when
additional loot is assigned to a given mob, elite, or world boss. (If RW has given GF the answer, GF hasn't passed it along to me.)
My guess is that each mob/elite/world boss/instance boss either has one or more "standard" items (durability is almost certainly random), and in the case of instance bosses, they have a chance to drop a given item from the loot table assigned to them, and those items are assigned when you and your party enter the instance and/or set the difficultly level. I'd say that additional items, such as monster cards, are dependent on a certain, unknown percentage value.
IS luck potions, housekeeper luck potions, luck buffs from guild castle buff towers, plusses to wings, and the Rogue skill "Treasure Hunter" are all supposed to affect loot drops. Do they stack? Do any of them overwrite any, some, or all of the others? I have no idea. I'd say, and I have no empirical evidence one way or another, that luck buffs probably do stack and influence loot drops, mainly by adding items to the loot that a mob drops, and possibly (unknown) affecting the durability of items. YMMV.
Or, it could be as you've already suggested--when the mob is killed. As I said at the start, I Don't Know. Your guess is as good as or as bad as mine.
A couple of years ago, a guildie convinced me to have a Rogue character character of mine to accompany him to AV so he could farm elite mobs and (hopefully) improve his chances of getting Magic Cavies to spawn. Now, that Rogue was fairly low level (~26 or so) and had absolutely no business being in AV. But I was bored and figured that it couldn't really hurt. That character's Treasure Hunter skill was 24 or 25 at the time.
He seemed to think that it made a difference. I can't say whether it did or not. I do know I got killed a bunch of times, even when I stayed in relatively "safe" spots, and in Hide. Thankfully, the rez point was fairly close by and I could usually get back to where he was without incident. I don't remember if he picked up very many, or any monster cards.
As for enhancement gems, I've found that I have absolutely
zero fails or level drops when I use them on the second Tuesday of the week.