That is a common misunderstanding in shops. Some think that the bacteria live in the water so water changes removes them. Yours seems to think that water changes kills bacteria but they will only do that if you don't add dechlorinator to the new water.
Ignore the shop. You need to do water changes as often and as large as necessary to keep the ammonia and nitrite readings well below 0.25. With a reading as high as yours, I would remove as much water as possible, leaving just enough water for the fish to be able to swim in. Test again after half an hour and do another water change if they are still above zero. Once the readings are down, check the levels a couple of times a day and do water changes as necessary to stop them reaching 0.25.
You said you cycled the tank then added fish, then you said you did a fish-in cycle. What fish, and how many, did you cycle with, and how many did you add afterwards? And did you add all the new fish at once? When a filter is cycled, it has enough bacteria to cope with the ammonia from just the fish in the tank at the time. When you add more fish, they will make extra ammonia and the bacteria have to multiply to cope with this extra. Adding a lot of fish at once makes a lot more ammonia and it can take a while for the bacteria to multiply enough to cope with all that extra.
As a very general rule of thumb, it is safe to add in one go the body mass of fish equal to a third of the body mass of fish already in there. I use the term body mass as, for instance, a one inch neon tetra has less body mass than a one inch tiger barb because of the shape.
Weekly water changes are for fully cycled filters. Your other tank that is OK with weekly water changes is cycled. The tank with high nitrite isn't, and needs more frequent water changes until it is.
