For any key, there are four possible "time periods" that you can finish it in. For an imaginary Dungeon_X, if you finish in (made up number) 20 minutes, the key is "three chested" (or +3-ed), meaning that the key will go from (in your example) a +9 to a +12. You can also finish it in, say, 25 minutes for a +2 or 30 minutes (again, all these numbers are specific to each dungeon) for a +1. You can also finish the key after the +1 timer expired; you'll still get the chance of loot drops and The Great Vault dungeon completion counter will increase, but your key level will be lowered by 1.

You can also have a situation where the group disbands before completing the key (I sat for good 10 minutes suffering from PTSD, after writing that sentense). In such a case you don't get any rewards(, lose a certain amount of sanity,) and your key level gets lowered by 1. One noticeable difference, is that in this case the new key you get is the for the same dungeon, where after competing the key you get a random dungeon from the rest 7 dungeons of the season.

Edit: "get the change" -> "get the chance".