To expand on the comment by closetnoc, its most likely a DNS issue. As he says it can take up to 48+ hours for all the ISP's like mobile internet and cable modems to "catch up". Generally the server to server traffic is quicker, more like 1-8 hours.
In interest of this question, here are a couple tips for this transfer situation and how to poke your ISP/Cache to get new site faster:
-- If youre planning to transfer, hit your domain zones and check the TTL. 2 days before transfer, make it low like 120 seconds. Turn off non-essential caches. Prepare querystring cachebuster for things like css/js/font assets. Basically, make a bunch of things "call home" more often. More likely to freshen client DNS and see new stuff after transfer. A couple days after things settle, turn back on the caches, remove the cachebusters, and increase the TTL to whatever it was.
-- In addition to DNS check sites, a way to browse your transfered site the fastest often comes in the form of a webproxy like proxfree.com or similar. You want to test with one that preferably has never accessed your site. Obviously don't use any admin areas or enter passwords while using these proxies, but they offer a fresh window to confirm it's online via new DNS.
-- If you are having trouble viewing the new version of your site, you can try to clear your OS & Browser side DNS cache. With Chrome that is easy, paste
chrome://net-internals/#dns in the address bar and hit "clear host cache". With Windows its kinda easy too, open "run" box and use command
ipconfig /flushdns then restart Chrome. Don't forget about
shift-F5 in browsers too which forces a refresh.
Hope that helps clarify the spots DNS would hang up while propagating your new site location.