Hi! Grats on the move to DO.

It sounds like you’ve done all you need to do (and some) to update the DNS to point to your new Droplet. Here’s a tutorial to double-check:

How To Point to DigitalOcean Nameservers From Common Domain Registrars

The DNS services we all use will cache lots of information for either pre-configured lengths of time (TTLs) or arbitrarily. This is why sometimes during a DNS update and propagation you reach the old IP but someone else might successfully reach the new IP. This cache can happen on your local computer, your ISP’s DNS servers, etc.

There are some handy online tools to see how the DNS resolution appears to the rest of the world:

https://www.whatsmydns.net/

This one I use all the time. And then if I need to dig just a little deeper, I’ll check out the tools on this site for any standard issues I may have overlooked:

https://mxtoolbox.com/

They have numerous tools related to DNS and mail, among others.

Hope this helps and please let us know if you have any other questions or feedback ;)