They don't spill very much feed when they use the rubber pans, and it's easier for them to eat out of the rubber pans so if they have an option I think they will choose pans over the poultry feeder.
Our pekin drake lives with the chickens and has no issues using the same poultry feeder you have. I don't know if it would be different for you since you have more than one though, I prefer to use a rubber pan for my ducks. I like taller pans since the ducks don't seem to want to step into them...