The fish more than likely died because your tank wasn't ready for fish yet. Let me explain.
Once the nitrogen cycle has completed which is introduce ammonia source 2ppm, wait until the nitrites start to rise, you will have both ammonia and nitrites at this point and the nitrates will begin to rise. At some point the ammonia will go to 0 yet you will still have nitrites and nitrates both. When the nitrites go to 0 and ammonia is 0 you will have nitrates and technically your cycle is complete and you maintain a sg of 1.025 to 1.026 The tank isn't ready to add fish at this point.
Next what needs to happen is to add additional ammonia to see if the nitrifying bacteria can process it to 0 ammonia in a 24 hr period. Either add a large dead shrimp or pure ammonia to reach 2ppm, also continue to ghost feed your tank as if it did have fish. This food and ammonia feeds the bacteria that are needed to process the bioload (ammonia) your fish will produce when they process their food through their system. Taking a poop.

Expelling waste.
At this time you've been maintaining the sg of the water, running your lights, ghost feeding as if you had fish and maintaining a constant temp you should be starting to see a significant algae growth If so Great, it's time to add your clean up crew CUC. The cuc will start keeping the tank clean and also eat much of that ghost feeding that you are still doing. But what I suggest at the point right before you add the cuc is to bring the ammonia up to 2ppm again and be certain that is processed to 0 in a 24 hr period prior to adding the cuc.
So now you have basically cycled the tank and can look to add fish. Lights are running, heater is keeping a steady temp, cuc is keeping the tank clean, you are ghost feeding the tank and adding daily top off with fresh RO DI freshwater for top off all of this every day to maintain the sg of 1.025-.026.
Now you can add one or two fish. You've gone to the lfs and picked out your two fish and bring them home, you need to acclimate their bag unopened to the temp of your tank. Simply float the bag in your tank for 10-15 minutes. Now open the bag and you can either drip acclimate or add about a 1/4 cup of tank water to the bag. Do this every 10 minutes for 30 minutes and now you can add the fish from the bag into your tank.
If you did not complete all of this prior to putting your new fish in this is why your fish died and the tang more than likely will either die for the same reason or will be very stressed and likely get ich. This brings up one of the reasons why to have a quarantine tank.
I'm not trying to scare you just let you know that NOTHING GOOD HAPPENS FAST in this hobby, it takes time. Patience will be well rewarded as long as you force yourself not to make impulsive buys or hasty decissions. This means plan out the fish you want in your system, add the least aggressive fish first the most aggressive fish last, By adding fish slowly at one or two every two to four weeks to allow the biological bacteria time to grow and adjust to the bioload your fish are introducing into the water. If you don't take your time doing this your system will crash and your fish will get sick or die. All of this is reason to setup a quarantine tank, but that's a whole nother thread.
In closing you are going to spend a great deal of time and money on what will become a very rewarding hobby as well as your pride and joy, don't rush it and don't needlessly kill livestock by rushing into it. The livestock and your wallet will both appreciate it.