How DNS works?

I got a customer who also has another hosting account from a different provider for the same domain name. They are using the other provider for backup purposes. The nameservers listed for their domain are:

ns1.ourdnsserver.com (our nameservers)
ns1.theirdnsserver.com (other provider's nameservers)

However for some reason, the domain is being directed to the other provider's nameservers first. Why is this? Our nameserver is not down. Is it just completely random which nameserver a domain is directed too?

 

 

 

 

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