Started using your mod. In the process of studying, they became interested in the function of turning manipulators, but did not understand how it works. Can you tell me?

That function will only work on inserters that insert into cargo wagons. How it works is that every time a train leaves, any inserters that are holding items get turned around so that they don't leave items on the ground that get put in the next train. The Dispatcher will automatically switch these inserters back once the next train arrives.

Conceptually, we understood this function, but for some reason it does not work for us. It was suggested that maybe it does not work with manipulators modified using the "Bob's Adjustable Inserters" mod, or manipulators should be connected to the dispatcher in a special way

As far as I've been able to test, it does seem to work, even if the inserters don't appear to have turned around. It's just that some inserters pick up more stuff after they've been checked and were empty

I'm not sure I understand you. English is not my native language. Just in case, I will describe that our manipulators were standing with the remaining cargo after the train left, despite the included function

1) That function will look at each inserter/manipulator one by one.
2) If the inserter has items in its hand, it will reverse their direction. If it is not holding anything, then they are left alone.
3) Sometimes, the inserters that were not chenged can pick up more items after they have already been checked.
That results in the behavior you see, where they still have items in their hand.

I hope this makes it clearer : )

No, unfortunately it has not become clearer. My friend and I watched the station with the manipulator turn function turned on and did not see them turn around and return the excess to the warehouse

Thanks for your interest in my mod. This function should work as Mr. Wristwatch described above. For which I thank him more.
The function should work fine with the "Bob's Adjustable Inserters" mod - I use this mod in my game.
If something is wrong, then it needs to be fixed. It would be great if you sent a save where the error appears. It would help a lot.

P.S. What is your native language?