For all the years I’ve used Coleman gasoline stoves I have followed the lighting directions by rote, and never had any problems with either getting the thing going or with flare-ups.
I’m not sure exactly what the lighting lever on my old Coleman two-burner gas stove does, or how. I do know the main valve regulates the flow of fuel from tank to (through) generator; the lighting lever operates some kind of choke mechanism, I suspect.
If you really are curious, you might take the tank and generator alone out into a wide open place, open the main valve to the lighting position, and observe what happens to the fuel stream when you move the lighting lever to different positions.
After the stove is running you will want to check the tank pressure (by how much resistance there is against the pump). It may need some pumping. When you start the second burner (only after the main burner is running well) you will notice the main burner flame dies down a bit. Open the main valve to compensate.
One reason I’ve always liked my Coleman gas stove is the simplicity of its operation. Even I can do it without running into problems.
G.