I don't think they're necessarily doing any special tricks with the painting or the software to make the colors like that (although the first link you showed, they most likely did put down a purple layer set to screen, soft light, or overlay to unify all the colors--but they may have just chosen those colors to start without any computer magic). I think instead they're planning out their colors before they start painting--like the 2nd link there, in particular, is really good at planning color harmony that feels like a lot of colors are happening, but when you study it, they're focusing on a few main colors and using slight variations of those colors to build form.
I can't think of any speedpaint for color theory off the top of my head, because they'll just go into it already knowing the plan, so you wouldn't see the step you're describing. Although, it may be nice to know how they maintain their neons if you're worried about your colors getting muddy.
When it comes to choosing color, what I like to do, is just like--steal the colors from people that do it well and analyze it close up (also keep the colors stored in my library so I can use them later in my own art)
So like this image from your links, which at first glance seems complicated as hell:
You can just take the color picker and see how many colors you get out of it saved to your library, and usually in pop art they'll reuse the same colors but in slightly different hues, and you can delete colors that are virtually the same. So after I did a bunch of choices in the color picker I get this:
And then you can blend it, since even after narrowing these down, they're still so similar I can just...simplify (also that green neon is virtually the same as the yellow neon so I'm going to ignore it for the sake of this study)
And then see a good idea of how it breaks down into color theory. The neutral orange/pink I think yellowed when I did the blur because my yellow stroke was so big, so you can see I went back in and chose one that's the more khaki to match the image before. But basically, they have a neutral pinky tan, offset by the purple/orange-pink in the character's hair--there's barely any green to detract from the purple orange, and when they use neons, it's an as accent.
So before I do a piece, especially one that is more abstract and less based on realism, I like to start do a little test where I make like...a Rothko basically. This isn't an art school thing, PS--I have no idea why I started doing this, or when, I just do this. I make big squares of the main colors I like--and a tiny sliver of the accent, just to see if it works and vibes in a way that I like (and so like here's it laid out with the colors we just made)
It gives you a place where you can test colors before the big painting, and if you stick to the plan and don't stray too far from your original palate, changing tint or hue to define the form, the colors will always vibe together, you already tested them.