One way of classifying languages is grouping them into stress-timed, syllable-timed and "mora"-timed languages.

Stress timed languages (like English) are ones where the time between stressed syllables is roughly the same. Take the phrase "I went to the store with my friend John". Most native English speakers will stress "went", "store", "friend" and "John". It might not be a big difference, but you'll notice the "to the" between "went" and "store" is rushed, and that there's a sort of gap between "friend" and "John" since both are stressed. (Also, if you were to modify that slightly and say "I went to the store with my friend named John", the time between "friend" and "John" wouldn't change much at all, you'd just slip "named" into that gap.)

Many Romance languages are seen as syllable-timed, where each syllable takes the same amount of time. In French that phrase is "Je suis allé au magasin avec mon ami John", that's 14 syllables, all roughly the same timing. In Spanish it's "Fui a la tienda con mi amigo John", 12 syllables. Unless you're really drawing attention to one of the words, every syllable there gets roughly the same timing.

Japanese is mora timed, which is pretty similar to being syllable timed, except that when you encounter double-letters they double the length of the syllable. So, "Just a moment please" is "Chottomatte kudasai", where the syllables with double-t letters take twice as long. The cities Tōkyō (two syllables), Ōsaka (three syllables) and Kawasaki (four syllables) all take the same amount of time to say because the "ō" symbol means that letter gets double the length of the standard "o".

The 4 most widely spoken languages in India are Hindi (way out in front with 44% of the population speaking it as a first language), followed by Bengali, Marathi and Telugu (with about 6-8% each) The first 3 are all Indo-Aryan languages, and Telugu is a Dravidian language. The 3 Indo-Aryan languages are considered to be syllable-timed and Telugu is considered to be mora-timed.

IMO, what makes Indian-inflected English seem fast is that they're adopting the syllable / mora timing from their primary language and using it in English. That means they spend less time on syllables / words that English speakers would stress and more time on the un-stressed syllables. The overall timing of what they say is probably similar, but in evening out the length of the syllables, they take time away from the syllables that other English speakers naturally slow down to stress. Since you tend to notice the stressed words more, since they're rushed it seems like the entire sentence is rushed.