Sounds like you have a better LFS staffer than most, recommending you wait before adding more fish. However, first thing to do is add more filter media from your 90l tank. You can take up to 1/3 from it without compromising the remaining bacterial colony. But also add more new filter media to that filter so the bacteria can work on it. One square inch of filter isn't nearly enough to cycle your new tank.
I'm confused as to why you'd have any chlorine in your water??? You should dechlor any water that enters your tanks. And switch over to Seachem Prime or StressCoat+ for a dechlorinator as they also neutralize heavy metals and ammonia from your tap water.
Do not get any more fish until you've cycled this tank. Shouldn't take long with more mature media from your other tank. Neons especially are sensitive to new tanks and should only be added to well established tanks. But since you rescued the ones you have now that couldn't be avoided. So adding more neons in a few weeks should be fine.
Get yourself a liquid test kit as well, so you can test your own water whenever you need. API Master test kit, Nutrafin or Salifert are all good. Don't get test strips as they're terribly inaccurate.
And please keep us posted!