I am going to attempt to turn some of our conversation into an answer.
In short, using chords that are not in the key of a song is (or can be) modulation as b3ko pointed out. But this, to me, is a specific device of western music. You are referring to a form of eastern music, Carnatic, from south India. The ragas of India do not all map easily to one of the diatonic scales of western music. In western music harmony can be achieved by using three distinct chords that are contained in the scale I, IV, and V (and V7). This doesn't mean that there are only three chords in the key, but that one can develop a 3 and 4 voice harmony using just these three chords. The standard treatment of including multiple voices with the same rhythm as the melody is called homophonic harmony. For this to be possible the melody needs to be structured and predictable. Indian music is highly improvisational and the improvised melodies using ragas take precedence over any other aspect of musical expression (based on my experience). Rhythm is important too but there is no "orchestration" in Indian music. The main instrumentalist (or vocalist) explores the melodic and rhythmic terrain using raga and rhythms as they see fit. In classical (or traditional) Indian music (and Carnatic music is quite old) the melodic support (harmony for lack of a better word) is achieved purely using drone notes, no actual harmony in the western sense takes place.
While modulation is a viable explanation for what you are describing, that could be seen as an example of Ethnocentrism (no offense). Using western music theory to draw a conclusion about Indian music attributes.
Based on what I've said about the use of chords that are in the scale and the fact that the ragas do not necessarily line up with western diatonic modes the question may not be fair at all.
I would ask you to do the following:
(1) Get the exact raga being used in the song you are listening to
(2) find the notes on a piano or guitar if possible (the western equivalent)
(3) first see if the chords you are describing actually use notes from the raga (If they do then they are actually in the raga and hence harmonically consistent with that raga, hence there is no "modulation" relative to this scale)
(4) if they do not fit in the raga ask yourself if there is a change in raga used that correlates with the change in chords used (maybe this is an Indian version of modulation), or ask yourself if the scale simply does not fit on the piano. In this case there may be no "western music theory" explanation for what is happening. We can get trapped into thinking that western music theory simply IS music theory but this is a horrible example of Ethnocentrism.
Many ragas can be mapped to notes on the chromatic scale but not the diatonic. Turkish music uses quarter tones in their scales and some Indian Ragas may as well. If this occurs then you cannot describe harmony using classic (church based) homophonic voicing. That whole paradigm goes out the window! You will not find quarter tones on a piano.
The rules of harmonization in western music are derived in part from choosing notes from the same scale to harmonize a melody. So I would say that if the chords are in the raga there is no modulation. We do sometimes add out of key notes for texture but in western music this is done on occasion. If you judge a raga by comparing it to a diatonic mode you may conclude that the melody is "always out of key". But again this is an example of ethnocentrism.
In the case of Indian - Jazz, or Indian - western fusion there may be no theoretical basis for the choice, just that some chords that are not offensive are chosen to complement the vocalist. I found your question interesting and I hope my explanations were helpful (or at least interesting).