There's a lot of hype around the quick start stuff. I use it myself to speed up a cycle - but I've never had a tank cycle in less than a month even with using these products. Having a diatom bloom doesn't mean that the tank is ready for a lot of fish all at once. It's really indicative of nothing. You'd mentioned using 1 piece of live rock and the rest was (dry rock?), correct? People typically cure dry rock before adding it to an active tank, for instance. This process takes about 6 weeks before that rock is live and ready to start acting as a filter in your reef system. Cycled water? Water doesn't really speed up the cycle since it filters nothing. Really, it just added dirty water in your tank.
Your bioload needs to catch up. This means that the filtration method you're using (rock and sand) need to continue to build beneficial bacteria to address any load increases. It takes time - quick start or not. Most people start off with one or two small fish once the tank has cycled, then a month later, you can double that and add a few more fish etc., all while building up more and more bacteria. If you overload the system, it can crash even if the tank was cycled.
Stress doesn't necessarily have to come from other fish - it can come from the environment as well, meaning that It can be caused from water that isn't pristine as well.
If this is the advice your LFS gave you (put in a bottle of quick start and add 10 fish a week later) I'd suggest not listening to them anymore and seeking the advice of this community. There are some very experienced reefers here who can offer you sound advice and coming to us is a step towards learning more about the hobby. We don't want to put you on the defensive - we've all made choices when we were newer reefers and were learning the hobby that were naive.
I'm concerned about the QT idea. Don't get me wrong - I'm not against it - I am concerned that you don't have media that you can use that will provide proper filtration. When I'm setting up a QT, for instance, I use pieces of marine pure from my sump to provide an instantly cycled QT. Since your tank is new, you won't have this unless you have an older tank that is still up and running (??). Do you know any reefers with established tanks that you could borrow media from? Even if you have to ask the LFS for something that has been in their system, I'd suggest this. Since you're treating these tanks eventually with copper or CP, you don't have to be concerned that the media carries ich. Personally I'd suggest copper (it shouldn't be an issue with the type of fish you have). Cupramine is what I use - tangs do exceptionally well with it. If you select cupramine, add the dirty media, put a half dose of copper as per instructions, let it sit for a few days to reduce contaminants from the dirty media, add the fish, keep it at a half dose for 2 more days so your fish get acclimated, then bring it up to a full dose.
You can't monitor ammonia while using copper (It screws up the readings and they look sky high) save perhaps a seachem ammonia patch that helps a bit, so it's important to have a well establish media present. Otherwise you'll have sick fish swimming in ammonia and it's a recipe for disaster.
