It won't work. Your technique has a fundamental problem that I'll explain below, but even if your technique was correct, some limitations of Blender's viewport will make impossible to produce the correct result.
Why the method you used wont work:
You say you used pre-rendered PNGs as source, and that's the problem.
PNGs use unassociated (often called "straight" alpha), which is inappropriate for compositing light effects.
The explanation is rather simple: A lighting effect, such as fire, electricity arcs, laser beams, etc.) is a purely emissive phenomenom, so itt's basically an addition (the light source adds luminosity but doesn't occlude any of the background).
When you use an unassociated alpha image (like your PNGs) every pixel with alpha > 0 will occlude the light coming from the background.
The phenomenom you're trying to reproduce shouldn't occlude any light from the background, so its alpha has to be 0.
But in unassociated alpha images, there is no RGB information where alpha is equal to zero, as that information is discarded by the alpha over operation for unassociated.
What you need is an associated image (often called "premultiplied), that lets you have RGB where alpha is equal to zero for this kind of effects, that need pixels that are luminous but don't occlude the background at all.
For that reason, PNG won't cut it.
The proper way to composite luminous effects:
If you use instead EXR images you'll be able to produce lighting effects that can be mixed with the alpha over operation as if they were a pure addition.
Just render your lighting effects on black, use a "set alpha" node to assign a 0 value (black) to the alpha channel and save as EXR, and you'll have some nice lighting effects ready to be composited.
Why it won't work anyway:
Blender's viewport, and to some extent cycles have some limitations regarding alpha manipulation.
The materials view does some funny things flipping between associated and unassociated alpha, which results in RGB with alpha zero being lost before it gets to your screen
So, even if you try to produce the right shader with cycles (which could work in the compositor), the material view will kill it.
Your best bet is cycles with a good GPU that can keep up the pace needed for realtime preview.
Since the phenomenom is purely emissive, you need an emit shader which is extremely fast to render, and the good news is that you need a few samples to get it rendered. Noise shouldn't be a problem (just use 8 for start resolution and one sample for preview, it will be fast and noise free).
The bad news is that cycles has some problems producing a proper output from a shader constructed with an alpha-driven mix where pixels have to be luminous, so you can connect the nodes in cycles to produce a luminous premultiplied image, but it won't render correctly.
But wait, there's hope! :-)
Not everything is lost: If your ligthing effects are purely emissive and you don't need any occlusion (which means, all your alpha will be zero), you can create the effect with cycles.
First you have to create an emission shader using the ligthing effects rendered on black background as texture, then you need to ADD that shader to a transparent shader using the add shader node.
The output will work in the cycles render view and it will be fast.
It won't work in the materials view, though. It will render white.