DNS is like the phone book of the internet. It ties names (atxcommunity.com) to numbers (67.255.188.166). If your ISP has a crummy DNS server and doesn't refresh its phone book properly, every time you go to atxcommunity.com, you'll get the wrong number and see the old site on the old server.
When I start the migration, it'll be late in the evening. I'll shut down the site and replace it with a message that says something like "we've moved to a new server. as soon as the internet does its thing, you'll see the site again" and then follow that with my contact info. If 12 hours goes by and you're still seeing that, then your ISP has unreliable DNS servers. Luckily, it's pretty painless to change two numbers in your router's configuration (although all routers are different so finding them can sometimes be tricky) so that you can use some nice, free, fast service from a 3rd party that you don't even have to sign up for. As an added bonus, they'll respect your privacy more than most ISPs.
I started years ago using Google's Public DNS because I had a crummy ISP. Cloudflare's service is faster, and I prefer not to put all of my privacy eggs in one basket so I switched. If there's some down side to using their service, I have never encountered it.