If any group of tetra is not grabbing the flakes either on the surface, or as they fall, I would not add more. Flakes settling on the bottom are just going to decompose, fungus, and add more ammonia to the tank. Few if any characins (there are some) will feed off the bottom.
On the feeding, fish frequently don't feed for perhaps several days. After all, moving to a new environment is a major upheaval in their life, much more than most of us can even begin to imagine. The differences in water chemistry will be very significant to a fish, and this affects their internal metabolism a lot.
Re the spitting out, it is difficult to say, but more usually the fish is actually biting off tidbits; especially if they repeatedly grab the food, spit it out, grab it again, etc. This is normal feeding for many fish, esp characins (tetra, pencils, hatchets).