Hello & Welcome to Fishlore!
My advice is to get your own
test kit. He said your water is fine, did he give you the readings? The best test kit is the
API liquid master kit, it tests for
ammonia,
nitrite,
nitrate and
pH.
It's great you got some fish but it would be a good idea to get at least 3 more Tiger Barbs as they are a schooling fish. It'll make them happier and better temperment toward other tankmates. Uping your Neons to 5 would be better too.
For the bottom you could do a school of 5 Corydora catfish and a Bristlenose Pleco and/or 2 Pictus cats with a Bristlenose. Maybe a school of Rainbow fish. They have nice color. If you want a school of fish that stay near the top you could do Danios. Another cool Tetra is the Columbian Red Fin, they get about 2.5", Serpae Tetra & Bloodfin Tetra, 2". Just thinking in the size range of your Tiger Barbs which is 2.5". Never mind the pictus, forgot you had Ghost Shrimp. lol
Check this community to build with Tiger Barbs.
http://www.elmersaquarium.com/c106community5barbs.htm