During the change of Name servers, DNS is cached at all DNS servers until the TTL (time to live) has passed at which point they should update with the latest DNS.
This can typically take >24 hrs for DNS to propagate throughout the Internet (depending on how the domain was previously configured), during this time you may have a crossover of traffic sent to your old server/s or your new server/s depending on the DNS server used and if it has been updated yet.
Please review the following suggestions to help purge your own network of cached DNS.
https://www.servwise.com/en/knowledgebase/489/Flushing-DNS-cache.html
