OK, time to bring in the pro water treatment guys.
Gary hit it way back in post #2. I'm pretty sure that what's happening is that the neutralizer is backwashing every 4 days, on schedule, and the septic tank can handle it, as long as there's nothing else going on. However, once in a while the softener decides to regenerate, and it happens to be a "neutralizer night". It looks like they set the softener to regenerate at, say, 2AM, and the neutralizer later -- at 4AM, maybe. (Setting the times apart by a couple hours ensures that only one valve is drawing water at a time. They're conscious of trying to draw too much water from the well to satisfy the high flow rates required during backwash, but didn't take into account the cumulative effect on the septic tank.) On these nights, the softener pretty-much fills up the septic tank, then the neutralizer kicks in and overwelms the tank and it backs up. You can solve the immediate problem by ensuring the two regenerations occur on separate nights. I don't know enough about the controllers to advise you on this. Ideally there's a way for them to talk to each other so that the neutralizer knows that the softener has claimed this night, and to wait another night to do its thing (or vice-versa), but I've never heard of such a communication link being available. My 2501 is purely mechanical, but fancier computer-controlled valves exist, and there might be a way to coordinate their backwash cycles.
Find out, if you can, the exact models of the 2510 and 5600 controllers, and whether the 2510 is mechaical or demand-driven. I suspect you've got a 5600SXT (with an LCD screen, computer-controlled), and the 2510 is mechanical (7 or 12-day "skipper wheel", no computer). I can imagine a simple controller that would signal the 5600 that it's OK or not-OK to regenerate, but there may be a built-in way to do that. But I are an EE, not a Fleck controller expert; the experts here can tell you if it's easy to do.
You may have a larger problem - the septic system. Your septic guy can tell you how much headroom -- the amount of empty space -- exists at the top of the tank, and should know how well the drainfield accepts the tank's outflow. If the drainfield is inadequate, the tank will fill up rapidly and drain slowly. But as I said earlier, the septic system is designed to handle "normal" residential loads. Whether an inrush of over 100 gallons in 3 or 4 hours is "normal" or not, I don't know. But the septic guy can easily test your existing system to see what its limits are, and since it seems to handle the everyday household load, you're probably OK for the time being. Just don't get any ideas about adding a giant whirlpool tub.