All tea originated in China. In southern Chinese dialects tea is called "Cha," which is where other languages got their "Cha" sounding word for tea, and this includes the Indian languages afaik.
The northern dialects' word sounded more like "tea" which is where the Western languages got their word for tea, through trade
You've got the geographic regions mixed up. Northern Chinese refer it to "cha", while Southern Chinese call it "te" (sounds like tailor). Even though India is geographically closer to southern China, they got the word from Portuguese.
It has nothing to do with its country of origin (I assume you meant China?).
0: https://en.wiktionary.org/wiki/chai#Etymology_2