How to film a strobe light
What you're seeing is an inherent problem with sensors that use "rolling shutter". There are tradeoffs in sensor technology among speed, sensitivity, and size, and using a sequential line readout with continuous exposure is a popular choice that's a good compromise for many situations. Unfortunately yours isn't one of those.

What you need is what's known as "total" or "global" shuttering, where the entire frame is exposed at once and read out as a single image. Instead you have a sensor that essentially exposes each line of the array at different times.

So I'm afraid the answer is: use a camera / sensor that employs a different technology. I hope for your sake someone has a solution that allows you to use your existing setup, but I don't expect to see one.