Both times I got it, I died, after doing a some damage to the enemy, and a few kills.
I think damages are counted, not kills as chadz said, so assists would count too.
Both times, end of the round, I died, and I Think I was the last of my team.
Both times, no upkeep.
Didn't saw the multiplier, but I didn't checked, I would have get it after the first tick as it's server related stuff.
My guess is when you do X time more damages to the enemy than you take (you're fighting, not hiding) and die last, you don't get any upkeep and you keep the multiplier.