...
You are now connected to Exchange Online with you Office 365 Tenant admin and can use Exchange Online PowerShell cmdlets available.
Prior to a move request being issued you need to verify the UPN field is correctly set to @tufts.edu
Now issue a remote move:
New-MoveRequest -Remote -RemoteHostName 'exchange.tufts.edu' -RemoteCredential -TargetDeliveryDomain 'tuftscloud.mail.onmicrosoft.com' -identity
you can verify that your mailbox has been successfully moved by doing a get-mailbox command