After you've repaired the alarm clock and are putting it back into service, you want it so that the alarm will go off when the hands show the the appointed time...or so that the hands show the appointed time when the alarm goes off. Here's the method I use. It works for any alarm clock I know of, mechanical or electric.

The alarm hand and time hands are off the clock. The alarm is in the "off" position. The alarm hand will turn counter-clockwise when being set. Using the alarm set button, turn the alarm hand arbor SLOWLY, just until you hear the "click".

Install the alarm hand, pointing exactly to 12:00. Install the hour and minute hands pointing exactly to 12:00. The alarm and time will now be very close.

Advance the alarm hand (counter-clockwise) until it points exactly to 1:00. Advance the time hands SLOWLY toward 1:00 until you hear the click. If the minute hand isn't pointing exactly at the 12, pull it off and re-position it exactly on the 12.

Advance the alarm hand until it points exactly to 2:00. Advance the time hands until you hear the click. If the minute hand is off the 12, remove it and reposition it. Repeat until it's as close as you can get it. A difference of 3 or 4 minutes between the time hands and the alarm going off is pretty good.