Hi John ,
Yes, this is normal behavior:
When a file is moving, it continues to appear in the source directory until it's fully moved to the destination and then it will be deleted. The file remains in the source sites Recycle Bin after the Move is complete and is subject to the normal recycle schedule unless a user recovers it from the Recycle Bin.
There are some information about move/copy to, please have a look:
https://mydigitalworkplace.wordpress.com/2018/05/20/10-things-about-copy-and-move-sharepoint-online/
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