In the real world, passengers know where they want to go, and cargo has a label with a destination written on it. In OpenTTD, this is not the case. Passengers and cargo happily jump on any train that accepts them, even if it brings them back to where they came from. This means, trying to set up a two-way feeder service as described in Feeder service by adding a passengers flow in the opposite direction, will fail. Passengers are unloaded first, and are then loaded back into the same train they just unloaded from.
You can make this work by adding a second station, as shown in the picture
. Passengers are being transferred from Lutway to Fludingville and vice versa. The trick is that each train unloads + picks up passengers from the city, unloads everything (without loading) at the first feeder service station, and loads new passengers at the second feeder service station. Since both trains visit the feeder service stations in opposite order, they unload their passengers such that the other train picks them up again.