"Someone at petsmart told her that they would be fine if she added “Quickstart” spray, instead of doing the traditional let the water sit for 24 hours thing. None of us knew better."
There's so much wrong with this I don't know where to start.
The Quickstart is different from water conditioner. Leaving water to sit overnight will eliminate the chlorine, but not other toxins that are present in tap water, like ammonia and chloramine.
When you add tap water to an aquarium, you need to add "water conditioner." This will neutralize chlorine and other toxins from the tap water. Forget about leaving it out 24 hours, that's the way they did it in the 60's. If you added Quickstart that did not neutralize anything, in fact it added more toxins.
Quickstart is to jump start the "cycling" process. Fish produce ammonia, which is toxic and will build up. Cycling is when beneficial bacteria form which eat ammonia and produce less toxic compound that can be diluted through water changes. If your tank is not cycled, ammonia and nitrites will build up and poison your fish. Cycling takes a month or so. It's a completely different function from adding water conditioner.
Either the person at the pet store didn't have a clue, or your mother completely misunderstood.
You should add water conditioner right away. You should also get an API Master Test Kit (with test tubes) to frequently test the water for toxin building, stay away from test strips. API Prime is a very popular and effective water conditioner. Personally, I've never used Quickstart or any of the other bottled bacteria. I think it's snake oil and doesn't work like advertised. Your tank will cycle in four to six weeks on its own without adding anything. But along the way you still have to test every day and do partial water changes with water conditioner to keep toxin levels low.