There is some fancy logic applied - too much to detail here. Here's a basic explanation.
All [muzzle] discharges are recorded and time stamped (with 1 mSec granularity) as are all shots received by a target. We know that a shot has been fired from a particular firing point, who fired it, when it was fired (to within 1 mSecs), at what it was supposed to be fired at, and subsequently when/if it arrives at its intended destination. Theoretically variations in times of flight between shooters can result in potential confusion at the target - basically a faster bullet overtaking a slower one that was fired first. But this turns out to be quite rare - we have been looking for instances of this for some years now. It happens, but as I said, it's rare.
When the shooter mound units are employing a wired LAN the mound units are able to syncronise their clocks (time) to the master clock to within 1 mSec. When using the wireless LAN (wifi) it is generally about 4 or 5 mSecs and somewhat variable (due to the vagaries of wifi). In any event, the time stamping of discharge events is rather precise, as is the time of arrival at the target. We use this to accurately measure the time of flight (that allows us to calculate average velocity).
So, if a discharge is recorded at a firing point that the system expects to see arrive at a particular target some time shortly thereafter, but instead appears at some other target (within the TOF window for the range) then that discharge is deemed to be a cross fire. That shooter is informed (on the screen) that a crossfire occured and is awarded a miss. A cross fire miss cannot be discarded or disclaimed. He/she is not told which target received the shot (that is, which target they actually fired at) - only that it occurred. Unlike with manual targets, whoever is supposed to be shooting at that target is not informed. There is no pair of "spotters" from which that shooter can select the best - if they happened to have fired. If they haven't fired then to them it's like nothing happened at all.
I guess to fully answer your question, unless the cross fired bullet collides with the legitimate shot at the target, or over takes it during flight, there is a pretty good chance that the system will "get it right" and record the proper result for both shooters. Experience has shown that it generally does - we have plenty of experience with crossfires!