According to this:
You can transfer time by grasping another person’s hand. The person with the hand on top gets the time.
After re-watching it definitely looks like the author is right. It looks like whoever has their hand in the top position gets the time. This also explains the success of the time thieves: Since there are 4 or 5 of them, all they have to do is hold someone down and force his wrist down and they will always get the time, no risk. The only reason Hamilton is able to beat the time thief at the end is that he agrees to a fair fight, this explanation also explains why a fair fight was required. Hamilton would have had no chance if 4 men bent his wrist down.
What "Time" is doesn't really come into play for the answer here, but since this is interesting to me: If I were going to design a post-human system, I would install a battery into human beings and use it to power the nanomachines that are certainly a requirement of how the post-humans in this story worked. As soon as the machines that govern the activity of the heart, lungs, perhaps the subconscious parts of the brain, etc., ran out of power you'd die. The amount of time left on a battery is the display, and the transfer of that charge is what is exchanged.