This is exactly what we would expect. Any ammonia produced in the new tank will be taken up by the nitrifying bacteria you transferred over in media, substrate, decor, etc. Zero ammonia and nitrite is good, and what you want to see going forward too. Nitrate at zero is not bad, because the ammonia may not yet have made it through the Nitrosomonas sp. and then Nitrospira sp. bacteria. And if the ammonia is minimal, from a few small fish, it may not result in nitrates at all, or in time low nitrates.
If you have live plants, this almost ensures zero nitrates at least for the present. All of my tanks run in the 0 to 5 ppm nitrate range, which means they could be zero or 5, but it is low enough not to worry.
As there are fish in this tank do not add any artificial ammonia, this could easily do something harmful if not deadly to the bacteria and the fish.