Hoppers ignoring chests when items are from container above

The reason the behavior is different when you put items directly into the hopper is because hoppers pull and push items out of and into other containers one at a time.

In the case of putting all of the items in the chest, the lower hopper always "pulls" the item from the upper hopper before the upper hopper can "push" the item into the chest. So, all of the items will go into the bottom chest. Many redstone builds depend on this behavior.

In the case of putting all of the items in the upper hopper, that hopper will be able to push some (half) of the items into the chest because the lower hopper only pulls one item from it at a time.

You might want to visit one of the technical communities on discord or reddit to ask about redstone mechanics.

If you want to design a system that will put half of the items from the first chest into each output chest, you can put two hoppers under the top chest and then redirect those into separate output chests.

As mentioned above, please go to reddit or discord and ask for help with redstone.
Or you might want to visit Community Support for help.