Then does anyone understand what are differences between push notifications and using a record until the TTL expires?
Thanks!
Push notifications occur when the primary is HUP'd or restarted, telling the secondaries to pull fresh zones so that everybody's is known to have the same serial. After this the secondaries poll the primary every 'refesh' seconds to check for a newer copy of the zone.
Take a look at: https://www.rfc-editor.org/rfc/rfc8765.html#name-push-messag...
That section contains most of the RRset remove notifications.