The sync speed itself doesn't change, as that is defined by how quickly the shutter curtains move, but what is happening is the trigger is adding a delay, which throws off the timing. What ought to happen at 1/200s is that the first curtain reaches the top, the flash fires, then the second curtain starts closing immediately from the bottom. However due to the delay the second curtain has started to close by the time the contacts close on the remote flashgun, blocking part of the frame and giving you a black bar.
The delay is caused by the trigger needing to decode the signal and close a switch to fire the flash. The length of the delay is depends on the brand, and sometimes how much battery power is left in the trigger, but what you describe is common for that brand of triggers. I used to always set my shutter to 1/160 to be on the safe side.