You install shiny new rotors and within a day or two the surfaces are orange with rust - it looks like you got bad parts. Almost always, this is completely normal. New rotors rust fast for a simple reason. Here is why.
The friction surface is bare iron
A brake rotor's braking face must be bare cast iron - a coating there would ruin braking, so it is left uncoated. Bare iron flash-rusts within hours of exposure to moisture - see why rotors rust overnight. New rotors also have their protective shipping oil wiped off before install - see clean new rotors before install - leaving the fresh metal wide open to surface rust.
It scrubs off on the first drive
The good news: that surface rust on the swept area is scrubbed off by the pads in the first few stops, leaving clean, shiny metal where the pad contacts. So a rotor that looks rusty sitting overnight is bright again a mile into your drive. This cycle repeats any time the car sits, especially in damp weather.
The hat and edges may stay rusty
The parts the pad does NOT sweep - the center hat and outer edge - can hold rust cosmetically, which shows through the wheel. Quality coated rotors resist this on the non-swept areas; see coated vs uncoated rotors. Bare budget rotors rust there faster but it does not affect braking.
When to actually worry
Fast surface rust on new rotors is normal and harmless. Only worry about deep pitting from long storage, or rust that causes lasting pulsation or noise - see how to prevent rotor rust. Drive the car regularly, and pair rotors with quality pads and fresh hardware.