Hi Gil,
I understand that you have concerns that a remote move moved the on-premise mailbox, instead of copying the mailbox data to the cloud mailbox. If I misunderstand it, please feel free to let us know.
As for your question “will this also "cut me off" the same way as Remove Move did?”:
The short answer is no. Cutover migration won’t remove the on-premise mailbox. It copies the on-premise mailbox data to cloud mailboxes.
However, in this case, Directory Synchronization (DirSync) has been enabled, Cutover migration cannot be used anymore. After DirSync is enabled, only Remote-Move, IMAP migration and Staged migration are available.
If we use Staged migration, here are two limitations:
1. Exchange 2010 or Exchange 2013 mailboxes cannot be migrated to Office 365 via a Staged migration.
2. After a single local mailbox completes a staged migration, all of the emails sent to the local mailbox will be moved (not copy) to the corresponding cloud mailbox. In other words, after a single local mailbox completes a staged migration, emails don’t come to the local mailbox any more.
As for IMAP migration:
1. An IMAP migration copies the mailbox data too and synchronize the data every 24 hours that is different from a Staged migration.
2. An IMAP migration only copies the Inbox data, not the Contact or Calendar data.
3. An IMAP migration only can be used to migrate mailboxes. Other mail objects, such as distribution groups and mail contacts, cannot be migrated to Office 365 via an IMAP migration
Thanks,
Claud