That is not exactly correct.
Pronunciation does not change. Enunciation does. Vaidika mantras do not follow the same rules as Tantric mantras, which is what primarily we discuss here when we say mantras (with Gayatri and Mrityunjaya being the exceptions).
For example, the famous Purusha Sukta is found in the Rik, Yajus as well as Atharvana Veda. The formation, the rules of enunciation are different between these. The words follow the same pre-Paninian Sanskrit, so the pronunciation is not different technically of the letters. Their enunciation is different as the svaras or intonation differ.
The three rules of enunciation - anudatta, udatta and svarita are defined differently not just between different Veda, but even between Shakhas of the same Veda (e.g. Shukla vs Krishna Yajurveda) - and these are passed on verbally across generations. And the enunciation differs between regions (Varanasi vs Kanchi, etc.)
Tantric mantras are less strict about pronunciation, but Nipun-type of quackery is unacceptable there as well.