Well now that we know what alternator you have it will be easy to wire the new one correctly.
The external regulator plug in the first picture is all you need to convert to the CS alternator . You simply run the brown wire to the L plug on the CS alternator and the red wire will run to the S terminal. The brown wire which is converted to the white wire in the adapter now goes to the L terminal.
I see you stated that the adapter plug is connected to the blue wire on the old external regulator plug. Was that a mis print or does it actually plug into the blue wire.
Here's how you tell. The correct wire will have 12 volts on it with the key on and nothing with the key off. That is the wire that goes to the L terminal on the CS alternator. The other wire will have 12 volts on it at all times because it is the sensor wire which is connected to the battery power. I would connect it to the S terminal on the CS alternator if you have a pin in the plug in the alternator.
Now here's the rub. The CS alternator requires at least a 35 ohm one watt resistor in the brown wire to protect the diodes in the alternator. This is well documented in all the conversions and The website below shows it as well as the diagram posted. Painless wiring recommends using an 85 ohm 5 watt resistor but the guy in the website used a smaller wattage and a higher ohm resistor which worked for him. If you don't have the extra resistor in the brown wire, that might explain the failure of the alternator.
Here's the website.........
http://temp.corvetteforum.net/c3/zma...ternator01.htm
Here's how I do it. This is for the SI series which does not need the resistor, the only difference is you'll need to add the resistor in the brown wire from the firewall.
This is for the CS wiring