Yes that is correct. When the name resolution process occurs, those name servers are listed as being authoritative for the zone. If the name sever cannot satisfy the request it send back that information to the requestor and the process will stop.
The requestor doesn't simply discard that response and decides to try another name server. The name server that is the ultimate authority on that zone already said there is no such record.
Ya I had updated already. I registered domain with same hosting company and they had their own dns on my domain, I used this domain as addon domain so I was unsure if I should update them same as main domain or it will be automatically done by hosting company. It had been just a day after buying hosting so I was unsure whether it was just because of new hosting or nameservers.
Your hosting company should be providing you with instructions on how to modify your DNS records for the domain that you own. Generally, they will provide you with information about the host (A) records that you will modify in your domain zone. Unless your hosting company also manages your DNS, it isnt going to be automatic.