Email-related DNS changes can begin working quickly, but full propagation depends on the TTL values already in use and on how fast outside resolvers refresh their caches. Some systems see the change quickly, while others continue using older values until cache expiration.
Because mail flow is sensitive to MX, SPF, DKIM, and related records, it is wise to make changes carefully and avoid overlapping conflicting records. During migrations, test with multiple destinations and allow enough time before assuming something is broken.
If you changed DNS very recently, propagation delay should be one of the first things you consider.