Yeah, www DNS caches are (I'm sure) registering latest host provider static IP for your website so this is "normal www behaviour" for a few days when you are changing hosts. Domain transfer is hugest www change (for one domain/website) and you always need few days for that to complete.
In that period you have 2 (here and there) "hosts".
Funny, depending on a location youre visiting your site, you can see actual site, or you can see old one - at the same time.
But old one will vanish in few days. Enjoy!