Why are you adding salt? It won't hurt your fish, but it's not likely to help anything, either.
I would concentrate on testing Ammonia, Nitrite, and Nitrate in the new tank at least every day, and doing huge water changes if you find Ammonia or Nitrite above zero. The new guy's finrot was likely caused by poor water quality in his last tank, and so putting him in a tank that's not properly cycled is going to worsen his problems -- just keep testing, and keep up on your water changes!
I would concentrate on testing Ammonia, Nitrite, and Nitrate in the new tank at least every day, and doing huge water changes if you find Ammonia or Nitrite above zero. The new guy's finrot was likely caused by poor water quality in his last tank, and so putting him in a tank that's not properly cycled is going to worsen his problems -- just keep testing, and keep up on your water changes!