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In the version of Mancala that i play, if the last stone of the move lands in an empty hole, the pieces in the opposite hole are "stolen" (removed and placed in the "thief's" home hole).

Must the hole have been empty at the beginning of the move, or can it have been vacated by the very move i just made?

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You are able to steal if the last piece lands in the hole it came from.

From wikipedia:

If the last sown seed lands in an empty house owned by the player, and the opposite house contains seeds, both the last seed and the opposite seeds are captured and placed into the player's store.

In this case, your last stone is landing in an empty hole on your side of the board, and the opponent's hole has stones. Therefore, you steal those stones.

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