Confused about when to convert units

The second is correct, and the first is incorrect. You're looking at the difference of two measurements (and the difference in Kelvin will be the same as the difference in Celsius). In your first line, you're making a difference into an absolute measurement and then converting it, and that is incorrect.

A difference in temperatures isn't a temperature any more than a difference of dates is a date. You may convert temperatures to temperatures using your formula. Your formula does not convert differences in temperature to anything at all (in the same way that applying any other wrong conversion fails to produce a difference in temperatures).

We have that

• $0 °C\equiv273.15 \,K$

and therefore for $T_C$ expressed in $°C$

• $T_K= T_C+273.15 $

therefore for $T_C=-30 °C$ we have

• $T_K=-30+273.15=243.15\,K$

and then

$$-30\,°C-0\,°C=-30\,°C=243.15 \,K-273.15 \,K=-30\, K$$