It doesnt really matter what type of lighting instruments you use, tungsten, hmi, led, flo, so long as you use the same color temperature lights to light the screen as you do to gauge the lighting of your scene and subjects.
I do a lot of greenscreen work, and my best "short" advice:
1.) Get as big a screen as you can afford. And get your subjects as far from it as possible. This will reduce back and side spill.
2.) Use 1/4 magenta CTM rosco gel for hair/cut lights, behind your subjects. The subtle magenta is complementary to green, and will give you a better key and better edges in post.
3.) Avoid stray hairs.
4.) Use best codec possible. 444, 442, 422 being the worst. I shoot RED 3:1 and still have issues sometimes.
5.) Test shoot, and do your key in post, before you shoot. If you have fast moving action, you will want to shoot at a higher shutter speed. Motion Blur can be a problem.
6.) It's easier to shoot at a higher f-stop, and get a sharper tack, and add back in blur/dof effects in post, than it is to shoot wide open with a long piece of glass. Blur causes masking issues.
7.) Get Keylight for AE.
8.) Have a dedicated waveform monitor if possible. You want your luma to be a straight line at 75 IRE. You will not be able to light your screen evenly by eye, you really need a waveform to get a spot on straight line, with no dips or falloff on the edges.
9.) Dont let your subjects wear green.