My personal opinion is that's velvet. It's possible that your original issue was velvet as well, and it persisted in your tank until you introduced new fish. However, without the ability to examine the fish in person and (especially) take a small tissue sample for examination under a microscope, it's going to be hard to determine. One thing that's a clue is the time between noticing the spots on your original fish and the fishes' death. Typically, marine velvet kills within 24 - 48 hours. Fish with ich will many times survive several infectious stages - they'll have the characteristic white spots, then seemingly recover with no white spots, then a couple of days later be covered and succumb.
I'm going to guess that you don't have effective medications on hand. Therefore, what I'd suggest is that you go to the local home store and buy 2 food-safe white 5 gallon buckets. Then drop by the local Petco or Petsmart and buy two cheap heaters, a cheap air pump, some airline, a package of inexpensive airstones, and (if you don't already have it) a digital thermometer. Heat new saltwater at a specific gravity of 1.015 to 78 deg F in one bucket; heat RODI or dechlorinated tap water to 78 deg F; catch the fish and place them in the heated freshwater for 3 to 5 minutes, no more. Transfer them immediately into the heated 1.015 seawater in the bucket, equipped with an airstone and a heater. Make sure that you watch the heater in the bucket carefully to ensure that it holds temperature but doesn't bake the fish.
Sterilize the other bucket that had the freshwater in it - a capful of bleach and a 15 minute soak will do it. Clean the bucket well, and set it up with new seawater, heated to 78 deg F, at a specific gravity of 1.010. Note that you must have an accurate refractometer to do this; anything lower than 1.009 will kill the fish. After the fish have been in the 1.015 bucket for 2 days, transfer just the fish (no water!) to the 1.010 bucket. Sterilize the other bucket, and set it up with another batch of heated 1.010 seawater. After the fish have been in the first 1.010 bucket for 2 days, transfer them again. Throughout this procedure, you should maintain a volume in the buckets of at least 3 gallons; this is to minimize the buildup of ammonia. Thoughout, you can feed the fish sparingly if they'll eat; remove any uneaten food after 20 minutes.
You need to do the transfers every 2 days for a total of 5 exchanges. Note that this is a modification of the usual tank transfer method specifically meant to target ich. Marine velvet has a slightly shorter lifecycle, and the more frequent transfers will help you prevent re-transmission of velvet and also manage the ammonia buildup. Ideally, you'll have gotten a 5 gallon glass tank from Petco, a bag of Caribsea arag-alive for the bottom, a bottle of bacteria (Dr. Tim's, Fritz, BioSpira, or any other bacterial product) and set up the tank at the start of the bucket transfer procedure. "Ghost feed" the tank with a little food when you set it up. It will have had 10 days to develop a reasonable nitrifying bacterial base, and you can do a 100% water change right before you put the fish in to ensure there's no ammonia.
Also, make absolutely sure the glass tank's specific gravity is no more than 1.012 when you transfer the fish from the last bucket ride into the tank. They can take a rapid drop in salinity; they can't take a rapid increase in salinity.
As a final note, and I'm sure you've realized by now, you can't keep marine fish in this day and age without at least a temporary quarantine setup. Fortunately, for small fish, the bucket trick will do the job, and they're not only cheap, they're easy to clean.