English (for various reasons) is kinda the only common language throughout India. There isn't actually one non-English language that you can learn and be understood throughout ALL of India, (e.g. if someone from the state of Punjab goes to the state of Tamil Nadu, they likely might need to speak English to understand each other though there are always exceptions to this) so English is very commonly spoken throughout India. As with any English speaking country, the language has changed within India and Southeast Asia over time (there is regional slang/expressions/colloquialisms unique to SE Asia like calling the 'truck' or 'boot' of a car the 'dickie/dicky'). Many of the other languages spoken throughout India are more strict in their phonetics, e.g. each syllable has a specific sound and doesn't change based on the surrounding syllables. Many English speakers who learn in India likely end up using this kind of speech pattern with English as well, leading to a different cadence in pronunciation than in other regions of the world. There are times it sounds faster, but pay attention and see if you can notice if the person speaking is using more syllables or pronouncing parts of the word you might skip over in the same word, but just faster.
I used to think they spoke English as a second language too but that isn't always the case. Indian English is its own valid dialect and is a learned way of speaking as a first language. (Source - married an Indian, traveled India, seen some schools there, saw kids/family members studying, etc..)