Yes, one would expect a Medieval Latin pronunciation for a text like this one. But we're allowed to let our imaginations run wild... what if Cicero or Caesar time-traveled a thousand years ahead?
This is how either of them would have recited the DIES IRAE, from the 12th century, in their standard and educated Latin accents.
Also adopted here is the organic rendition of final -m: nasalizing the preceding vowel, and influenced by the following consonant to be pronounced either as a dental ([n]), labial ([m]), or velar ([ŋ]). If final -m is found in isolation, or followed by a vowel, the preceding vowel is nasalized and lengthened.
This is, then, my rendition of the way an educated Roman would've recited the DIES IRAE during the Classical period.