DoTs apply their full credit over time instantly for the full value of the DoT. DDs apply their full credit instantly (obviously)
For example in classic:
2 Envenomed Bolts on Efreeti Lord will take credit.
You cannot undo credit once applied. First to higher than 50% (>= 50) damage total will take credit for the NPC.
There is no such thing as overkill. Credit is applied to the mob's total HP pool. So if you nuke w/ Ice Comet, and you deal 55% of the mob's health in one hit, and the mob has 43% health remaining, you won't take credit. I think there's an exception to one shotting mobs which I could be wrong about.
So the idiot with 6 necros at a spawn where you only need 3 necros is wasting those 3 krono'd accounts for that era, provided he can kill the mob quickly with the 3.
If you DoT a mob at 43%, the same applies. Your EBolt may take, say, 41% of the mob's health in a single cast for credit. But if someone's already claimed 51%, you lose credit.
When you account for HP regen, the credit is still applied to the person who gets 51% first, I believe. Correct me if I'm wrong. NPC Gate doesn't count, as it clears 'credit' tables.
I believe non-pet NPC engagement (ie; guards) functions differently and removes credit for experience/loot but only if the guard takes the killing blow OR the guard steals 51% of credit OR the guard deals more than the mob's total health in one hit.
Reapplication shouldn't redo credit, but to be honest, I've never tried. Too long of a recast normally. Generally, just have 2 necros or shaman parked somewhere, ebolt, then if it's contested congrats, you've won 50% credit. Or an SK with HT would work to instantly apply massive damage, then follow up with an ebolt cast if contesting against another person. Provided your ebolt goes off first, you win.