I hope I explained that well enough to understand. What I'm asking is if, let's say, a Yungoos reaches level 20, but it's nighttime. When it turns to daytime, will it still evolve even if it's level 21 or above?
Yes. If you level a Pokemon up past the level it starts to be able to evolve at, it should evolve the next time the requirements it needs to evolve are met when it levels up.