It's well established that vowel length was phonemic in Latin, and that it played an important role in poetic verse. It seems probable to me that it also mattered when singing, but do we have evidence that it was? Or evidence to the contrary?
Some current languages drop some otherwise phonetic aspects of their pronunciation when singing. For instance, while Cantonese or Vietnamese, which are tonal languages, do take care to match tones with melodic contours in songs, Mandarin Chinese does not, and tones are largely ignored when singing. Japanese has phonemic vowel length, and largely keeps its while singing, but things occasionally get squeezed or stretched to fit with the music's rhythm, and geminated consonants occasionally get replaced with a lengthening of the preceding vowel (as you cannot carry a lengthy melodic note on a consonant).
So I could imagine Latin song lyrics strictly keeping vowel length and rhythmic length in sync, or maybe doing syllable length the way poetry does, or starting there but occasionally bending the rules a little, or doing away with that altogether and letting the musical rhythm dominate. But do we actually know how such things were handled in classical times?