I think in general people try to design their edge spot colors to contrast strongly with the color of the chip, so they'll often go with complementary colors for the chips and spots (check out this tool and the different colors that come up with complementary/triad/tetrad color groups:
https://colorschemedesigner.com/csd-3.5/) and achieve contrast with brightness/saturation as well.
In your first example with the $1 chip with a base color of light blue, the warm colors (yellow/orange) pop with it because they're on the opposite side of the color spectrum. The orange is darker (a bit more saturated and less bright) so it contrasts well against the blue background and is immediately visible, and the yellow and white act as light accent colors to support/highlight the orange color and make the chips look more interesting. White and blue are traditional colors for $1 chips as well, which I think heavily factors into the color choices for these chips.
It looks like they opted for colors with less contrast in hue on the $5s, but the darker red/brown spots are still easily seen across a poker table because of contrast in brightness/saturation so the individual chips would still be distinguishable in a stack. In that case the pink is just supporting the darker edge spots and helping those stand out more by leading to a greater difference in brightness between the dark spots and the areas around them (almost like a reverse dropshadow). The red hue for the $5s is also a traditional choice that people have come to expect for that denomination.
It's also important to think about adjacent denominations (like $1s vs $5s vs $25s) to avoid color schemes that might lead to dirty stacks, so usually chips that appear next to each other in the progression avoid reusing any colors at all so that it's clearer which chips belong to which denomination. If the edge spots of my $25s for example are close to the background color of my $5s, it's possible that people could get the chips mixed up and think they're betting $5 when they're actually throwing in a $25 chip.
Chip colors are fascinating, and the more I get into them the more I think it's inevitable that I'll have to design my own custom set.
Hope this helps! Cheers