The timer begins when the cursor first touches the first piece that you move -- not to be confused with the first piece the cursor touches. If the cursor just moves over one piece to get to another for example then that does not trigger the timer starting. However, if you do move the piece, then the time started the moment the cursor touched that piece whether you selected it or not. The timer ends when you put the last piece in position to achieve checkmate. Whether you officially dropped the piece or not is irrelevant, once its in position the time stops.

Atari 2600 / VCS - Video Chess - Quickest checkmate - 01:22.136 - Roger 111