When you update a DNS record for a domain, it takes time for the change to take effect. This is because of DNS propagation. It is the period of time that ISPs across the world take to update their cache with the new DNS records.
Because we cannot control when other ISPs will update or how long they cache when we change a DNS record, there is a period of time where someone in North America may pull the new record, and someone in Europe will pull the old record. The general rule of thumb is 2-24 hours before the world is all on the new record. It is all very hit or miss though, as this can be as short as 2 minutes, or as long as 48 hours.
While these sites are not 100% accurate, they will give you a good picture of how things are going, and it’s something you can show a client by sending them a link to the results. Play with it a bit when you get a chance.