Can I put stuff from inventory into my rented storage container in my house?

So I've invested 10 contribution points and placed a Storage Access Container in my house. When I use it, I can pull stuff OUT of my storage to my inventory just fine, but there doesn't appear a way to do the reverse.

I.e. my inventory closes when I open the container.

Am I missing something painfully obvious, or is this just not something one is supposed to be able to do?

The rental container chest for housing is simply to access your storage from there instead of having to go all the way to a storage npc to access. There is a bug with the storage container though, that when you open it. the storage's inventory is sometimes behind your inventory. Just click the top of your storage window and move it around to reveal the other storage. Hope this helps!