The yellow light provides a period when drivers know the light is going to go red soon, all else being equal this light should be set to stay on for just long enough for drivers in properly maintained cars, who drive at legal speeds, to see it and all either come to a stop or pass the intersection before the light turns red. Typically formulas care about the allowed speed of cars, the expected braking capability of a car that's allowed on the road, the gradient (down hill it's hard to stop quickly!) and other factors, plus the size of the junction (a huge junction can't change as quickly because it takes time to cross the junction).
That is, Sally is doing 40mph in a 40mph zone, she sees the light turn yellow, and she's very close to the junction so she just keeps going, everything is fine. Bob is doing 25mph in a 55mph zone, he's some distance from the lights, they turn yellow, Bob stops normally as the lights turn red.
With red light cameras providing revenue there is an incentive to cut that time too short. Now Sally finds the light turned red earlier and she got a ticket. So next time Sally won't make that mistake, as soon as the light goes yellow she slams on the anchors, and somebody goes straight in the back of her - there's a traffic accident even though we invented these lights to reduce accidents. Oops.
Now a _good_ government would resist the temptation. They would set the formula to reduce crashes. But money is very tempting. Shaving a second off the time, getting $1M of extra revenue and oops smashing up a thousand people's cars, that's a good deal so long as you aren't paying for all those car repairs...