Files changing during the course of migrations are very commonplace. To facilitate this Movebot has a delta feature that checks both the source and destination for changes by modtime and only transfers new or modified files.
Delta Migrations can be enabled on all migrations or you can choose to launch a delta sync specifically. Deltas, like reruns can be launched as often as you need and are generally much faster than full migrations.
Movebot does not perform delete or move operations on the destination so even with the Delta functionality, it is important to ensure major restructuring does not occur in the source during migration.
For more information on delta migrations see our blog post here.