Following the regulations, there is nothing like a primary and secondary DNS server. These indications are quite misleading but many systems adopted it this way. We only list the DNS servers as primary and secondary, because this is what the providers write on their pages. The bad phrasing is supported especially by how Windows handles it. If you look at any Linux distribution, there is usually no separation between primary and secondary, but you can only provide a comma-separated list of DNS servers on a par.
Indeed, you can not trust that a primary server will be the only one being used even if it is available all the time. It depends on the implementation in the system you use.