The free version doesn't support rename detection, so will copy the 'new' folder (in the new location), yes. If you have it set as a Mirror profile it will also delete the same folder from the old location (because no longer in that location on Source) so sounds like you don't.
Note that even the commercial versions only (optionally...)support potential rename/move detection as part of SmartSync (on run-2 and later) because it needs a previous-state-database to be able to check that d/b to see if any likely candidates exist. Be aware that any such candidates are hashed (to make 100% sure the contents match) before any rename/move actions take place, so can be slow (possibly as slow as delete & re-copy would be anyway)
Note that even the commercial versions only (optionally...)support potential rename/move detection as part of SmartSync (on run-2 and later) because it needs a previous-state-database to be able to check that d/b to see if any likely candidates exist. Be aware that any such candidates are hashed (to make 100% sure the contents match) before any rename/move actions take place, so can be slow (possibly as slow as delete & re-copy would be anyway)