This is called spill, and its a constant challenge. Sometimes its pretty straight forward, other time it can be very involved to deal with.
However, to explain it. I might just have to walk you through the process of chroma keging.
When you seperste actors from the green screen, its essentailly just artsy math. I'm sure you're familiar to at least some extent, the way computers express colour, by combining red green and blue. There are essentially 255 values for each colour, and an example of a colour might be R078 G221 B023.
There is another value you, and this is called an alpha, and it ranges between 0 and 1. This is how computers deal with transparency. 0 being transparent, 1 bring opaque, and anything in between a varying degree of "ghosted".
When we chroma key, the entire image has an alpha value of 1. So the green screen, the props and the actors are all opaque. If I were to layer the green screen footage over the cg footage. You would still only see the green screen footage because it is fully opaque.
Next, I start the process of picking certain RGB values and changing their alpha value.
So I could say 000R 255G 000B should now have an alpha value of zero.
All of a sudden. Any green in the image disappears, and the CG background will start showing through. The problem is. Every single pixel on screen had some green in it. So even though the green screen night be close to fully transparent now, say 0.02A my actors and props are now probably at least 0.85A. And the cg is showing through the actors as of they were ghosts.
Remember that I need them to stay fully at 1A.
This stage in the keying process is called making core mattes. Essentially, I want to get the bulk of my actors into the 1 range. And the bulk of the green screen I Into the zero.
After which I will refine them.
Now back to your actual question.
So what happens if the actor is standing next to the green screen. And it is illuminating him with a very green hue?
Well remember, all I really care about right now is getting my 0-1 alpha set up right now. I can mess around with the colours of the shot as much as I want, and then just extract the alpha values and re apply them to a crisp unaltered version of the footage. So I'm probably going to play with the green levels in the shot until I've sucked enough out that even though the green screen looks less vividly green. The characters face has almost no green left in it.
Imagine the background was 100% green. And the actors face had about 20% green spill. If I reduce the green levels of the stop by 20℅ the actor now has zero percent green and the background is at 80.