Overexposure is a function of your camera. The sun puts out quite a bit more light than a StarFlash yet cameras can be set to expose properly with this condition. I suspect you are using an automatic mode on your camera, which looks out at the world in front of it & sees a low level of light. So it tells the camera to expose for that low level of light, totally unaware that you will surprise it with a burst of light from the StarFlash. There are some techniques with certain cameras for using through-the-lens metering combined with an on camera system, but the way most people use remote studio strobes is with their camera set to Manual. Then use a flash meter to give you the correct exposure.
Before digital cameras, a photographer could test their exposure with Polaroid tests & waiting a few minutes for the “rapid” film to process. This cost about $2.00 per shot & was done for medium format cameras using film.
Another method using digital cameras: With digital cameras, you can take test exposures for free & just erase them once you get your exposure set. Try setting your camera in manual to f8 at 125th or 60th. [The shutter speed will only affect the ambient light exposure & for the strobe only needs to be within the range of the camera, which is frequently 250th & slower-which means for some situations that you want to mix ambient light, it will work fine on a tripod with slow shutter speeds.] Do a test exposure & look at your camera’s monitor screen & then look at the histogram. If the image is dark, dial your f-stop to a larger aperture (smaller number,) if it is too bright & the histogram goes off the horizontal scale, dial your f-stop to a smaller aperture to let in less light (larger number). Ideally, your histogram should extend almost, but not quite the full horizontal scale of the graph.
This technique will get you started, and then you can work on lighting ratios and creativity with multiple lights & reflectors.