You should submit this as a bug to Microsoft. It is beta software which means that there will be bugs.
If you receive them on your other computer you are downloading to a pst and not leaving a copy on the server. You get notified on the 2010 pc, but it disappears before you can read it because it gets downloaded on the other PC. This isn’t a “bug” it’s a “feature”. Outlook is working as designed. If you watch your inbox on the 2010 pc you will see the mail appear and then immediately disappear as the other pc grabs it and downloads it.