Unfortunately, the people in the shops give some of the worst advice imaginable, especially if it's a pet store that happens to sell fish. Even true fish stores aren't that great with the advice they give. If you keep the water quality where it should be the neons will probably be fine.
As for SafeStart (or any bacteria in a bottle products), they claim to contain this bacteria but without a food source, ie. ammonia, then they would start to die off immediately after being placed in the bottle. Not to mention the temperature extremes these products go through during shipment and storage. In the summer, the inside of a trailer can easily reach 120F or higher. Warehouses are the same, especially the closer to the ceiling you get. And then in the winter, it's in the other direction.
Even the bottle tells you to do something that is totally unnecessary. Using it after a water change is not necessary since there are no (or only miniscule amounts) of nitrifying bacteria present in the water column. Nitrifying bacteria are attached to everything in the tank but mainly, the vast majority are in/on the filter/media. That is where the most food is present as ammonia & nitrite are passed through the filter. Obviously, in a cycled tank you would not ever see measurable amounts of those toxins but there is always a very small amount.
The only way you every really suffer a bacteria loss is if you do something to the filter such as changing media (if you have carbon in your filter now, replace it with some other media as soon as possible) or if you have a hang on back filter, changing the filter pack or treat with a medication that kills the bacteria colony. So they are telling you to use their product at a time when it s totally unnecessary (just like filter companies tell you to change the filter every 2 weeks).
I mentioned carbon. It is primarily a mechanical filter. Most of us only use it to remove medications from the tank after treatment. Some don't even do that and simply do extra wter changes to dilute it. It really becomes saturated in anywhere from a day to a couple weeks and isnt doing anything for the tank other than providing a home for the bacteria. When you change it, you basically are throwing your biological filter away and putting your tank in a mini-cycle. And when you have to treat a tank, you have to remove it, putting the tank in a mini-cycle at a time that you least need to have water quality issues.
Last but not least, you mentioned that the test results have been fine. Do you mean that ammonia and nitrite hae both been zero nything other than that isn't fine even though some test kits list what that call a "safe" range. Any measurable amount of ammonia or nitrite is dangerous.