Bitcoin miners can construct the block header, including the timestamp, however they want, as long as it adheres to the consensus rules. The shift you describe is well inside the 2 hour timerange, so it can be done when setting out to mine the block. It cannot however be done once the block is mined as the timestamp is part of the header, which is hashed into the PoW, hence changing the timestamp would invalidate the proof of work.
Most miners however prefer to increase/decrease the timestamp in order to have a simple way to alter the header, thus more hashes to compute. This is sometimes called time-rolling and is performed on top of the nonce-rolling.