Blurring can occur with or without an external strobe.
Blurring of a photo subject can be caused by movement of the camera while the shutter is open and/or improper focusing.
The probability of getting blurry pictures should decrease as the shutter speed increases.
One common mistake that novice UW photographers make is that they don't depress the shutter button halfway to allow the camera to do its auto-focusing and auto-exposure metering. When this occurs, the shutter speed and focus will almost certainly be suboptimal. It's easy to imagine how this results in blurring.
Another common challenge that some users encounter is trying to take pics in low light -- something that divers often have to deal with underwater. The auto-exposure function of the camera will "read" the scene and determine that a large aperture and slower shutter speed is required to take a properly exposed photo. Move the camera a little too much while the shutter is open, and it's easy to see how this results in blurred photos.
A dedicated focus light that clicks off when the strobe fires and shutter opens might be helpful. This would facilitate both auto-focusing and auto-exposure metering.
FYI, all of my above recommendations assume that the camera is working properly. Obviously, several different kinds of defects could be responsible for image blur.
FWIW, some photographers who intentionally desire some blurring in the photo to represent dynamic change, e.g., speed of a car, car headlights traveling down a road, will actually set the shutter speed to be slower than the scene actually warrants.
