Any kill you get (not from one of your tag streaks) counts towards doubles, triples, etc.
If you're trying to get a psycho, I don't think you're going to get one... it's one of those things that just sort of happens. When the opportunity presents itself, you have to have the skill to kill 5 people who happen to be relatively close to each other. It's as simple as that.
(If the enemies are too far apart, you're not going to be able to get one no matter how good you are, so there is a lot of chance involved...)