When an MTA needs to deliver mail, DNS is part of the routing decision.
For a normal domain, the sender looks for MX records, orders them by preference, resolves the selected exchanger hostnames to addresses, and attempts SMTP delivery.
DNS failures are not all the same
A temporary resolver failure should not be treated like authoritative proof that a domain has no mail service. SMTP and DNS both distinguish temporary conditions from permanent ones.
Cache behavior matters
Resolvers cache answers according to DNS TTLs. After a migration, different senders can legitimately see old and new answers for a period of time.