Your photos are probably fine. The part left sticking out is the film leader, and many cameras are designed to leave the leader outside the canister after rewind. That does not mean the exposed frames are still outside.

If only the leader was exposed to light when you opened the camera, the images on the rest of the roll should be safe inside the canister. In general, light only damages the film that is actually exposed to it, so opening the camera after the roll has rewound usually affects only any film left outside the cartridge.

Why it didn’t go all the way in: some cameras rewind the leader fully into the canister, while others stop with the leader left out for easier handling.

Practical tip: if you want to avoid confusing a shot roll with a fresh one, you can manually wind the leader fully into the canister before sending it for processing.