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When I had my birds, they were making a mess of the food too. I had to regularly clean not only the bottom of the cage, but I also had to clean the floor outside their cage. It didn't mean they do not prefer the food when the food is everywhere. The only thing it prove is that these birds = messy eaters. You also can't use the behavior of dog to judge your birds. They are different creatures. Even different individuals of the same species can do the same thing while not for the same purpose.
For the question of "limit",
I am not expert on birds even though I have had them for years. The way I did was to provide enough food for them all the time. They would stop eating when they are full. I know that's not the way with dog, cat, or fish, but birds are different since they are small creatures with a lot of surface area to body mass ratio, and they have to keep really high body temperature, they do need to eat all the time. Since I was feeding them millet and veggie, they can't get fat from those food.
It has been almost two decades since the last time I had my birds, so I can't remember exactly. I used to fill their little bowl twice a day with millet. They seemed to be very hungry every time, since they were so eager when I was able to add more millet.
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