DNS and domains
DNS propagation
Why a changed DNS record shows up at different times in different places: resolvers keep the old answer until its TTL runs out.
"Propagation" is a slightly misleading word. Nothing is pushed anywhere; the authoritative servers answer with the new record the moment you save it. What takes time is the caches: every resolver that looked the record up before the change keeps serving the old answer until the TTL it was given has expired.
So right after a change, one person sees the new site and another the old one, depending on which resolver they use and when it last asked. A resolver that has never seen the record gets the new answer at once.
To check where a change has arrived, ask several resolvers directly and compare their answers with the authoritative server's. When they all agree, the change is through. If one resolver is still wrong after the old TTL has passed, it may be enforcing a minimum TTL of its own, or you may have more than one set of nameservers answering differently.