They'll sneak in the odd question here and there. Maybe they'll find out from the surname, or perhaps the locality of the town/city you're from in India, or the kind of food you eat (upper-castes are mainly vegetarian), or your dialect. Heck sometimes the deity you worship will reveal one's caste.

But then what? They talk down to you if you are a lower caste? In what ways does their behavior change if they know your caste? If they talked down to you and you told them that you don't appreciate their tone, then what would happen?

Yes, they talk them down, berate them more often, mostly involuntary cues of rejection. Most people would not talk back for the sake of being passed over for promotion/raises. I understand most Westerners wouldn't balk from the idea of talking back at them, but cultural norms in Asia effectively discourage back-talk against superiors, hence why it has been prevalent in SV for this long.