Few things come to mind on a new tank. How did you check the salinity? Refracto or hydrometer? Secondly, what brand is the ammonia kit? I would go check your water again now and see what the levels are. When crazy stuff like this happens, I will typically check it twice at the same time. (just fill up 2 vials instead of 1), just to make sure the reading is coherent and that you didn't mess something up when putting drops in. As to the flow, what are the placement of the powerheads in the tank? can you see the water surface being disturbed by them? Also, a few other things. Did you dump the contents of the bag( water and all) into your tank? If you did, that may not solve anything but never do it again. You always want to net/ scoop the fish out. Lastly, did you measure the salinity of the water in the bag before you started adding tank water to it? This is a crucial step. I run my tank at 1.026. I dont' add fish often over the last 18 months, and the last fish I got , I checked the bag salinity and it was at 1.020. I'm assuming you added the fish directly to the DT. I'd advise setting up even a small QT tank, and then you can better control the salinity level. For my last example, I lowered the salinity to 1.022, and added water to the bag the same as you. You want there to be as little of a jump as possible. Moving a fish from 1.020 to 1.026 within 30 mins to an hour is way too fast. I know in your example your tank is at 1.024 , but unless you tested the bag it came in, there is no way to tell how big of a salinity jump the fish went through. Unless they were on there last leg before you put them in your tank, I would rule out any sort of disease, infection, etc killing the fish within 1-2 days. Post as much as you can about your tank and I'll try to offer additional guidance as best I can. Did you use RO/DI water for the tank initially, etc.
Edit: Additionally, 1-5 nitrate on a newly cycled tank seems unusually low to me. My 125g which was an upgrade for 2 tanks into 1 with live rock established for over a year got up to 60 nitrate within a few weeks.