No, it's not the joker valve or the flapper valve
Yes, there SHOULD be a vented loop in the system if the toilet flushes overboard, and it is in the right place. I suspect you aren't flushing long enough in the dry mode, so the water that's left in the line between the toilet and the top of the vented loop (or if there is no vented loop in the system, between the toilet and tank, if it's uphill to the tank) WILL run back downhill. But, if your toilet is more than a few years old, there is another possibility: it just doesn't have the "ooomph" to push it over the top of the loop any more. Any manual toilet that's working anywhere near factory specs can move waste at least 6 linear feet or 4 vertical feet in the dry mode...but over time seals and o-rings wear out, reducing efficiency--which why toilets should be rebuilt every few years...but eventually, the inside of the pump cylinder also becomes so scratched, scored and worn that rebuilding no longer does much good. So your problem is due to one of two causes: 1. not pumping long enough in the dry mode...or 2. your toilet is so worn that it couldn't push all the water over the top of the loop if you pumped it all day. However, even if you do pump long enough and the toilet can do it, there'll be a little water left to run back downhill, but there shouldn't be more than about an inch in the bowl.The condition of the joker valve only determines how FAST it flows into back into the bowl...if it hasn't been replaced in at least a couple of years, the slit isn't a slit any more, it's a hole that'll let water pass through it quickly. But even a brand new joker valve won't block slow seepage. From your comments, it doesn't sound like the water is running back into the bowl immediately--that it's taking a while to do it--so your joker valve seems to be in at least decent, if not good, shape.Btw...why'd you look on the Raritan site for info about a Groco toilet???