@Scubajayz I hope I can help shed some light on this (pardon the pun). I have a Sony A6000 that I shoot underwater in a Nauticam housing. I had Sea & Sea strobes, but after what is a long and unrelated story, I have replaced them with a pair of Inon S2000 strobes. (I have not yet dove with the Inon strobes.)
There are a number of factors which come into play here, and I will try to address what I can based on the information that I have.
First:
You are correct. The A6000 flash sync speed is 1/160th second. That is the fastest shutter speed that you can set the camera if you are using the flash. This can be an issue if you are using only the built in flash, but is much less of an issue if you are using a strobe or even better yet, a pair of strobes. As
@RyanT mentioned, the strobes put out a lot of light in a very quick burst. For all practical purposes, the flash duration becomes the effective shutter speed.
Here is a good article that describes it. It is discussing above the surface photography, but the principles remain constant.
Second:
If you are using one strobe augmented by a video light, then things get significantly more complicated and you could be seeing some motion blur introduced as the 1/160th second becomes a factor with the light from the video light.
Third (and final):
If you are using only video lights to supply your additional light, then ignore the flash sync speed of 1/160th and shoot what gives you the best exposure.
