This is working as expected. The tab key is not a "shift right" key, it is an insert. It inserts sufficient whitespace so the first non-whitespace after the selection moves to the next tab stop. Note that this is a normal insert, ie any selection is replaced by the inserted text. This is normal behaviour for any insert, by typing, by paste, by the tab key.
Simply select a vertical line before the text you want to move, ie where you want the insert, don't select the text you want to move or it will be replaced.
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