Corrections to Altitudes/Heights
If you are under radar control, there is no need to correct for vectoring altitudes. If you are cleared for a full procedure approach (complete with procedure turn) but you are under radar control, there is no need for corrections for procedure turn altitudes It is good airmanship to be aware of what the correction is, in case of LossComms or automation difficulties.
If using BARO/VNAV andyou are within the temperature limit of the approach, you may descend on the vertical descent path established either 'managed, VNAV/IAN' without having to make any corrections, however; it is a good idea to know what these corrections are (in the case of DME fix or FAF), in-case there is a failure of the automation and you're able to maintain a vertical descent using an alternative method (VS).
What MUST be done is: The DH/MDA/DA must be corrected for temperature for the approach, otherwise you could reach minimums and actually be below the obstruction clearance altitude (due to altimeter error).
If the OAT is colder than the Limit Temperature, the procedure cannot be flown using the automation and an alternative approach would be selected using a constant descent profile...good old VS!
Previously I mentioned referenced Regulatory material...ICAO is NOT regulator, it provides Standards and Recommended Practices (SARPS). From ICAO's documentation and technical publications, performance engineers and procedures engineers develop approach profiles that meet local regulatory requirements.
I hope that helps.