Different birds feed from different areas, in my experience. Big birds can’t perch on the feeders, so they eat from the trays; and small birds don’t get to eat from trays as big birds monopolise them.
If you already have a seed feeder, a winter seed mix will probably include sunflower seeds in it. If you’re looking to attract finches, you will specifically need sunflower hearts (sunflower seeds that have been cracked open and the husk discarded, AIUI) and you will need a sunflower hearts feeder for them. It’s a very fine mesh feeder. A normal seed feeder I think doesn’t suit the way finches eat, and wind and birds knocking the feeder will spill a fair bit in the ground.