Every time my cat box runs to clean one of our cats seem to be in an emergency to poop.. The cat box can sit all day and not clean but the minute it starts up he must poop. I normally lock him up in the bathroom so he doesn’t run around finding places to poop. This only happens when the cat genie runs a clean cycle. I have tried to set it up for different times of the day but that doesn’t work. Nor does having it run at night he will still just poop on clothes or a pillow. Like I said he is the only one. I have another cat that waits until it is done cleaning.
Of course cats prefer their boxes to be clean. Some cats have such a strong preference that they will hold it until the box is cleaned, to the frustration of their owners who don't want to clean the box twice in a row. It may be that your cat is one of these types, and has gotten a strong association with the box being cleaned, and going, to this unpleasant result.
Another possibility is that it is simply being stressed out by the box's cleaning cycle, and going as a result.
My first suggestion is that you really should have more than one box, especially if you have multiple cats. That way, a box will always be available, even if one is being cleaned.
The other suggestion is to simply replace the automatic litter boxes. Owners like them because they hate the task of cleaning the litterbox, but they really aren't ideal for the cats. At best, the cats will tolerate them, but I think many cats seem to actively dislike them. And as convenient as the automatic boxes seem on the surface, they aren't really all that convenient if they discourage cats from actually using the litterbox.