Using a new Gloxy 990 on a Canon 80D hot shoe, the bright red light of the Gloxy Focus Assist is appearing on the image at a wide range of setting. The light works at half press - but must be firing again with the flash?
Why do you think that? I'm not sure what you are seeing, but I think the assumptions are all wrong.
Focus (and also focus assist) work during focus, before the exposure (at half press, not at full press).
The "red" focus assist is surely infrared (and much brighter than we can see), to which the exposure is not even sensitive to, if it were to occur at exposure, which it doesn't.
If the hot shoe flash is on the hot shoe, and turned on and ready, then it MUST flash with the shutter exposure. That's what flashes do. They flash when you work the shutter. Anything else would be very disappointing.