The only thing you might need to do after installing a new A/C compressor is:
* Recharge the system: This is crucial. After replacing the compressor, the refrigerant has been lost. You'll need to evacuate the system (remove any remaining air and moisture), and then recharge it with the correct amount and type of refrigerant (R-12 for a 1990 Seville, but this is now illegal in most places due to its ozone-depleting properties; it's likely you'll need to convert the system to R-134a with a proper conversion kit). This requires specialized equipment and is best left to a professional A/C technician.
* Check for leaks: After recharging, the system needs to be checked for leaks to ensure the refrigerant doesn't escape. Again, this requires specialized equipment.
In short, there's no "computer reset" involved. The only "reset" is getting the A/C system properly recharged and checked for leaks. Improperly recharging the system can damage the new compressor. Have a professional handle the refrigerant handling and system recharge.