Do you know what exactly this 'trop water' is? Some shops sell RO water (reverse osmosis) which is water that has had everything dissolved in it removed. The problem is that no fish in the trade can survive in pure water so minerals have to ve added back in, either by mixing with tapwater or by adding remineralisation salts. The amount of salts added make the water soft (only a bit of salts) or hard (lots of salts). What I'm wondering is, is the shop selling RO water that has had some minerals added back in to make it safe for softish water fish, which is less hard than your tapwater. I would be inclined to give them a ring and ask, but don't be fobbed off by some vague thing like it's water that your fish would be happier in.
The only downside to using this 'trop mix' is that you will have to use it all the time or the difference between it and your tapwater could cause problems for the fish if ever you have to use tap for an emergency water change. Ammonia and/or nitrite in the tank water when you have fish, or the fish are showing unusual behaviour, or you've had an unexplained fish death all need big water changes and if you couldn't get to the shop you'd have to use tapwater
Nitrate result - if the tester is a liquid one, one of the bottles will say to shake it hard before use. All the makes have a reagent which settles out and has to be shaken really well to redissolve it. The only difference between brands is which bottle. Just making sure you did shake the bottle in question really well
If you have zero nitrate in the tank, you will have to add it for plants to do well - I do know that much
pH - I know you said the tank and tap pH are the same, but just in case I would leave a glass of water to stand overnight and test again. pH often changes on standing. Since you used the 'trop mix' it will be different from your tapwater and you need to know what the tapwater does on standing.
Do you know exactly how hard your tapwater is? It should say somewhere on your water supplier's website. There are many fish that 'need' soft water that actually do well in hardish water, it's just that they won't be able to breed. Other fish prefer it hard such as livebearers and Rift Lake cichlids (if ever you decided to go for a rocky, plant free decor)