Yup, corrosion can happen extremely quickly with carbon steel!
After your shave the FIRST THING you need to do, before dealing with cleaning your brush, or making your face smell pretty with aftreshaves, etc, is TO CLEAN AND DRY YOUR RAZOR!
This is not an issue with the razor as it came to you, as it came clean and oiled. It does not take weeks or months for a razor to rust, it takes only hours.