I'm glad you found the article helpful!
So in ritual life, many Sanskrit terms are shared (because of religious texts and oral traditions in religious life). Terms like mantra and prasad are definitely understood across linguistic groups. There might be some variation (for instance, in Tamil, we say prasadam (I am Tamilian, so I can speak for that at least). Furthermore, some languages that are not originally related to Sanskrit (i.e. Telugu, Tamil, Kannada, Malayaalam) have borrowed a lot of words from Sanskrit (some more than others). Of course each language has their own terms for activities related to ritual as well.
But to answer your question, these terms would indeed be familiar to a family that speaks Telugu.
I hope that is somewhat clear...
If anyone knows more about this, please chime in!