Most mayflies are either light or temperature sensitive or some combination of the two.
What follows is a combo of good research that's out there and some good old shooting from the hip hypotheses filling in the blanks. But it's how I view things. And whether technically correct or not, it seems to work.
For hatches, water temperature is a key indicator, but it's typically "temperature days" since they hatched from eggs. So an especially warm day in December means as much as a warm day in May. And an early or late hatch last year started the clock earlier or later as well. They mature faster when the water is warmer. When they reach maturation, they hatch. That's what affects whether hatches are early or late, compared to previous seasons. A sudden warm spell can indeed fill in that last bit of maturation. But a sudden cold spell won't just stop everything, there's momentum. When those nymphs are mature, they're gonna hatch, regardless.
As for time of day, it's a combination of water temperature swings and light for when the "emergence" takes place (I won't say emerg-er!)
After they are duns, they fly to trees and molt into spinners, and wait to do the mating swarm thing. This is largely light dependent. When light levels reach a certain level in the canopy, they take off, and seek out lighter areas. Lighter area in nature = the break in the canopy over the water! In our world, though, it could be that, or a break in the canopy over a road, or a streetlight.
Then after mating, they become less attracted to light in general, and become more attracted to specifically polarized light. Such as the reflection of remnant sunlight or moonlight off a water surface (or, again, a nice smooth road surface will do it too).
Whether that's all perfectly correct or not, I dunno. But it certainly is true that sunny = later hatches and spinner falls. Cloudy means things can get going much earlier in the day.
Other hatches have some intracacies. For instance, tricos. Instead of waiting till it's dark enough for spinner fall action to begin, they wait till it's light enough. In that case, it starts earlier in the morning with blue skies. And later under clouds....