Different devices, same messages!

I am working on myself but I have trouble not grasping that the email I just looked at on one device is going to be the same messages even on a different device.  

I have read that people have trouble forgetting what they are doing if they walk through a doorway.  I think that is odd and I suspect my eyes tell me I have passed into a 'new' place and therefore expect things to be newish.  When I use a different device, parts of me probably expect new things, including new messages that I haven't seen.  

One of several factors that attracted me to Google software was that it was available on Microsoft, Apple and other devices.  So, logically, I would think that I would expect my list of messages to be the ones I just finished looking at on that other device.  I expect streamed movies to be the same but it takes alert reminding to expect messages will be, too.