No, the new Download Management features are a native element of iPadOS/iOS13 - and cannot, to my knowledge, be disabled.
You should always consider “move” to be an unreliable feature when attempting to transfer files between disparate file-systems; it is always safer to copy - and then delete the source file when you are certain that the file has been successfully copied. A file move within a single file-system is, generally, relatively safe (but not foolproof). Seasoned System Admins will always favour copy/delete over move where reliability is critical.
I hope you find this helpful.