The addition or subtraction of 273.15 is not actually a unit conversion; it is a scale conversion.
As units of heat, 1 degree Celsius = 1 Kelvin (and also, 9/5 degree Fahrenheit).
Addition or subtraction enters the picture because when we measure actual temperatures, we do it relative to a base point that is different for each scale. When we say it is 30C outside, we really mean it is 30 degrees Celsius above the freezing point of water, which is another way of saying it is 303.15 degrees Celsius above absolute zero.
So if you have a temperature measured in the standard Celsius scale -- e.g. "it's 30C outside today" -- you would add 273.15 to convert it to Kelvin. But if you have simply a quantity of degrees Celsius -- e.g. "the temperature increased by 30C overnight" -- the quantity is exactly the same in Kelvin.