First of all, I think the 2 days figure is outdated. I've seen it take UP TO 48 hours, but standard now is more like 4-8 hours. Also, because of the nature of DNS, your computer may see the dns resolve hours before (or after) your phone does.
Anyways, the answer to your question boils down to the concept of propagation. The DNS server you update has to tell all the other DNS servers out there about the change. The other servers only request an update once the TTL has passed, and those numbers can all add up when you're talking about all the DNS servers around the world.