What DNS propagation really is
Nothing is pushed across the internet when you change a DNS record. Your authoritative nameservers start serving the new value immediately. What takes time is that recursive resolvers, the servers your visitors actually ask, keep the old answer until its TTL runs out. Each resolver cached it at a different moment, so each one switches at a different moment.
That is why two people can see two different versions of your site for a while, and why a change with a 300 second TTL settles in minutes while one with an 86400 second TTL can take a day.