The birds eating in those photos are goldfinches, and bullfinches. The larger bird with the pinky-red breast is a male bullfinch.
The tray simply screws into a socket in the base of the feeder. I have some other feeders, and they have sockets beneath them, but their sockets are not compatible with the screw thread on that tray. I bought that combination from Pets at Home.
As I explained, I put the 'rejected' seed into another feeder, anticipating that that might be eaten, and not wasted. What has happened this morning is that 4 birds are around the new feeder eating the fresh seed, and the the old porthole feeder, which is full of 'rejected' seed, is being ignored.
It occured to me that the 'rejected' seed might simply be husks. You can get a lot of mess with the husks of some sunflower seed. That does seem to be the case for niger too. The stuff being discarded by the birds is probably not seed (although the odd seed may be there). This seed supplier explains this:
http://thebirdsbistro.co.uk/store/straights/niger-seed
So the tray doesn't actually save any food. And if you let the stuff fall to the ground you are not actually wasting anything.