You can kill pulsars at any time, whether they're pulsing or not. They will kill you if you enter into their lane while they're pulsing. They can also kill you at the end of a level if they've reached the top - they'll behave like flippers.
Pulsars do make the edge lines disappear for the lane they're in - it's a handy way to know where you can/can't move when you're focusing on action close to the near end of the tube.
I'm not positive of this, but I don't think pulsars can kill you by contact until the end of the wave (when they're acting like flippers). I frequently 'kamikaze' myself in front of them when they're near the top, and don't recall ever being killed (unless they're pulsing of course).
One of the most important things when dealing with pulsars, is to get into a rhythm with your movement, moving and shooting when they're not pulsing, then hiding out in a safe lane when they are pulsing. Related to this in my opinion is the necessity to learn how to kill flippers when they've reached the top and are flipping - you just can't cover everything when you're movement is constrained. I spent several months retooling my Tempest game, getting the timing down, but it's well worth it and even more important when you reach yellow and have to deal with multiple fuseballs.
One other thing which I've recently noticed, you can sometimes control the direction of movement of pulsars with your movements, sort of like how you can control barrels on Donkey Kong. For example, if there's a pulsar on your right, you can move to the right and coax the pulsar to the right (away from you), if you time your movement correctly. I need to take some video too!