Cody, do you have a way to tell us what your ISO, aperture and shutter speed were?
Also, are you shooting pictures that require daylight such as wide angle photos angled up towards the surface during daylight?
The way strobes work is by firing so quickly, even a really fast shutter speed is plenty long enough for the light to get in to the sensor. In practice youll find that 1/125 to 1/250th of a second is the fastest you can get with some rigs, due to delays in the system firing the flash, but very modern cameras are making it so you can have some models where way faster speeds are possible.
And in that 1/125th of a second, the red light which appears very bright to your eyes, does not really output very much light compared to the flash. The flash outputs, lets say 10 watts per second, but in under 1/125th of a second, so its really like a very short burst of 1,250 watts of light. But the red light is measured in watts per hour, and there is not much of a fraction of an hour in that 1/125th of a second. So, while the shutter is open, a lot of white light from your flash should be getting to the sensor, while very little red light does. So you can affect the amount of red light that comes in by changing the shutter speed or aperture, but changing shutter speed wont have an affect on the intensity of the strobes.
But I have had many times happen where I did use a slow enough shutter speed that some red light came in. The trick is to pick an aperture that lets a good amount of light infor very dark areas where I want the most light in, I might use full power flash and a lower aperture to let more light in, but otherwise, I might only use ¼ power on the flash to let me have much faster recycle times, and a high aperture to get sharper photos, and then you change the shutter speed based on the amount of environmental light you want. So for wide angle reef shots, you might need 1/60th of a second, but for macro work, you can go up to the highest speed that doesnt result in a black bar along the bottom of your shot, such as 1/125th of a second.
Of course, the best is to shoot in raw and edit in light room. You should be able to remove any little bit of red that is captured that way.
Post some of your shots, show off your handiwork! Solas are amazing huh?