He said it was running, so backwards battery terminals is unlikely.
When you say 'shorted itself' what do you mean? There was a straight circuit from the B+ heavy red wire on the back of the alternator to earth?
I have a 98 960/S90 which will be similar though not necessarily the same. With the engine and everything turned off disconnect the heavy wire from the back of the alternator, it will be hot/live so be careful. Read voltage from red wire to engine earth and red wire to chassis earth then red wire to battery neg post. They should be about 12V within .1V of each other. Also check battery pos post to the body of the alternator with the big wire off, and then the red/hot wire to the alternator body, should be 12v same as above. Sounds like you may have done this already.
Check the D+ small wire connector to the back of the alternator. Is it the correct wire/connector? Find a wiring diagram check the colour code of the wire/s. I cannot think of a reason for the alternator to just fry up like that though maybe, big maybe, if the exciter/small wire was to earth then it may do it. The archives are a good start for a wiring diagram, https://ozvolvo.org/archive/
Did you swap the voltage regulator when the alternator was swapped or is it the one that was on the replacement already?
