Well, the approach is to try to perform post weld heat treatment (PWHT) below the original or specified tempering temperature of the material. The main reason is to avoid any noticeable drop in mechanical properties after the completion of PWHT. Typically, PWHT (if required) of welded components is to provide for adequate stress relief and softening of the weld deposit, and weld heat affected zone without significantly altering the bulk properties of the material.
If you notice, most ASME material specifications for normalizing and temper provide a minimum value for tempering temperature to achieve desired mechanical properties. Increasing the tempering temperature of the original heat treatment by 50 deg F, provides for margin during PWHT to assure that you do not over-temper (or soften) the material away from the weld heat affected zone.
Advantages of the slightly higher tempering temperature - no real change in bulk properties of the original material (away from the weld) if welding and PWHT are required for fabrication.
Disadvantages - none really, other than working closely with your steel supplier on the front end of an order to meet your target tempering temperature requirements.