The Thunderclap rune of Fists of Thunder adds the ability to teleport to the target when striking it.
Does this teleportation happen on any hit of the skills 3-hit sequence, or only on specific hits in the sequence?
The teleport is only on the very first hit in the sequence. If you continue to use this skill, every third hit (after the first) will teleport you.
Even so, the mobility it grants you is absolutely insane. You won't have to manually move in combat again.