Animated shows are meticulously storyboarded before production begins. By the time the voice actors come in to record their lines, there will be a video rough cut of the keyframes (animatics) that everyone can refer to. After the lines are recorded, they are synced up to the animatic and passed down to the animators. From there, the animators proceed to create the actual animation based on the animatic.
For songs like in Disney movies, the storyboard artists will get an early version of the song that they use to plot out the action to match up with the music.
example below:
Voices always comes first, otherwise how would the animators sync up mouth movement to the voices? It also helps the animators create a believable performance, as they can let the emotions in the voice guide the acting choices they take when posing the characters.
For an example of recording voices after the action is done, look at any sort of dubbing (anime, foreign movies). The voice artists will try their best to match the mouth movements of the original footage, but it’s never going to work perfectly.