Yes you are correct. There are specific rules and boundations for chanting mantras, to get the full benefit from it.
Rules of Chanting
The duration of each tone is fixed and one should chant the manra according to the swara with each syllable stressed to the required extent, and each tone (for the corresponding syllable) chanted for that duration.
Chanting should not be done like singing, or like reading. It should not be muttered fast, each syllable should be properly uttered with the required stress and pronounced with clarity.
While chanting one should sit with his back upright, and not shake or move while chanting. Chanting should be done with a fixed posture to allow the complete effect of the sound energy. While this rule in general applies to singing also (say for instance classical music), it applies even more rigidly in case of chanting a mantra.
Whether the mantra is chanted aloud or internally, it should be done along with the swara.
If we check the second rule (while chanting one should...) it is clear that if we apply it as a ringtone it can ring anytime during (sleeping,bathing,etc) also some mantra's are restricted on some places (samshan bhoomi, street, public places etc). Even after all this if we take too much precautions and want it to ring (or even to play) we will not be reciving any cosmic energy as we are not creating the sound(naad) of the mantra's , we are not always sitting in the prescribed procedure...
There are restrictions to some mantra's like mahamrutunjay mantra, durga saptashati mantras etc are that:
If you are reciting it you should not stop in between chants and you should sit on clean and dry asan (made of kush, kambal(wool),or mrug charma[not possible]).
Talking about gayatri mantra, it is a starter for sadhna and is used by bramhin's to amplify their energy. It is clearly a disrespect of gayatri mantra or any vedic hymn if we set it as a ringtone or play it anywhere at any-time.
Remember there is difference between bhajans and mantras. we can set bhajans as ringtone but not mantras as mantra's are energy sources.
If we think of mantras as Sun, bhajans are as lamp. You can lit lamp anywhere but you cannot make sun go here and there, you can just derive energy from sun in correct manner with correct techniques.